Dear Students
Ingenious techno Solution offers an expertise guidance on you Final Year IEEE & Non- IEEE Projects on the following domain
JAVA
.NET
EMBEDDED SYSTEMS
ROBOTICS
MECHANICAL
MATLAB etc
For further details contact us:
enquiry@ingenioustech.in
044-42046028 or 8428302179.
Ingenious Techno Solution
#241/85, 4th floor
Rangarajapuram main road,
Kodambakkam (Power House)
http://www.ingenioustech.in/
Wireless Sensor Network Based Clustering Architecture for Cooperative Communi...ijtsrd
We propose clusters based cooperatives based verbal architecture coop on the cellular ad hoc wireless sensor network Mawsn with the environment fading Rayleigh. The main ability and contributions of this paper are as follows. First, the proposed cage uses a cluster as a underlying system to help stable transmission services. 2D, the proposed enclosure uses a cluster based verbal cooperative exchange to effectively guide the package delivery ratio with multi hop power saving transmission. 0.33, we do not forget reasonable methods mainly based on cellular ad hoc nodes with sensing features and constant sensor nodes in the sensor field along with conventional research for the introduction of constant network sensors. Fourth, we have theoretical analysis with blackouts opportunities for proposed cooperative transmissions. Overall performance evaluation is run through simulation and evaluation. Sweeti Kumari | Dr. Ranjan Kumar Singh "Wireless Sensor Network Based Clustering Architecture for Cooperative Communication" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd43670.pdf Paper URL: https://www.ijtsrd.comengineering/electronics-and-communication-engineering/43670/wireless-sensor-network-based-clustering-architecture-for-cooperative-communication/sweeti-kumari
SHADOWING EFFECTS ON ROUTING PROTOCOL OF MULTIHOP AD HOC NETWORKSijasuc
Two-ray ground reflection model has been widely used as the propagation model to investigate the
performance of an ad hoc network. But two-ray model is too simple to represent a real world network. A
more realistic model namely shadowing propagation model has been used in this investigation. Under
shadowing propagation model, a mobile node may receive a packet at a signal level that is below a
required threshold level. This low signal level affects the routing protocol as well as the medium access
control protocol of a network. An analytical model has been presented in this paper to investigate the
shadowing effects on the network performance. The analytical model has been verified via simulation
results. Simulation results show that the performance of a network becomes very poor if shadowing
propagation model is used in compare to the simple two-ray model. Two solutions have also been proposed
in this paper to overcome the effects of shadowing. One solution is a physical layer solution and the other
one is a Medium Access Control (MAC) layer solution. Simulation results show that these two solutions
reduce the shadowing effect and improve network performance.
AN ENERGY EFFICIENT DISTRIBUTED PROTOCOL FOR ENSURING COVERAGE AND CONNECTIVI...ijasuc
As wireless sensor networks (WSNs) continue to attract more and more researchers attention, new ideas for
applications are continually being developed, many of which involve consistent coverage with good
network connectivity of a given area of interest. For the successful operation of the wireless Sensor
Network, the active sensor nodes must maintain both coverage and also connectivity. These are two closely
related essential prerequisites and they are also very important measurements of quality of service (QoS)
for wireless sensor networks. This paper presents the design and analysis of novel protocols that can
dynamically configure a sensor network to result in guaranteed degrees of coverage and connectivity. This
protocol is simulated using NS2 simulated and compared against a distributed probabilistic coveragepreserving configuration protocol (DPCCP) with SPAN [1] protocol in the literature and show that it
activates lesser number of sensor nodes, consumes much lesser energy and maximises the network lifetime
significantly.
Interference aware resource allocation model for D2D under cellular network IJECEIAES
Device-to-Device communication (D2D) has emerged as an efficient communication model in future generation cellular network for offloading cellular traffic and enhance overall network performance. D2D communication aid in attaining better spectrum utilization, lower delay, and less energy consumption, which can well adapt to meet demand of higher transmission rate, larger network capacity. Further, enhances spectral efficiency by reutilizing resource. However, it may result in severe cross-tier interference and co-tier interference. Therefore, efficient interference modelling design are required to address performance degradation caused by the interferences. The existing model has focused on addressing interference considering D2D association operating on same cell with the cellular association. As a result, it incurs interference to the cellular user located in the same cell. However, practically D2D association in overlapping area will reutilize spectrum of multiple neighboring cells. As a result, it incurs interference in multiple cells. For overcoming research challenges, this work presented Interference Aware Resource Allocation (IARA) model for D2D under cellular network as a game theory model. This work consider a resource allocation game where base station as a contender for catering D2D resource needs under different assumptions. Experiment are conducted to evaluate performance of IARA. The outcome shows IARA attained significant performance improvement over state-of-art models in terms of sum rate (utility), successful packet transmission, revenue, and delay.
Extending the longevity, is a significant job to be accomplished by these sensor networks. The traditional routing protocols could not be applied here, due to its nodes powered by batteries. Nodes are often clustered in to non-overlapping clusters, so as to provide energy efficiency. A concise overview on clustering processes, within wireless sensor networks is given in this paper. But it is difficult to replace the deceased batteries of the sensor nodes. A distinctive sensor node consumes much of its energy during wireless communication. This research work suggests the development of a hierarchical distributed clustering mechanism, which gives improved performance over the existing clustering algorithm LEACH. The two hiding concepts behind the proposed scheme are the hierarchical distributed clustering mechanism and the concept of threshold. Energy utilization is significantly reduced, thereby greatly prolonging the lifetime of the sensor nodes.
ON THE PERFORMANCE OF INTRUSION DETECTION SYSTEMS WITH HIDDEN MULTILAYER NEUR...IJCNCJournal
Deep learning applications, especially multilayer neural network models, result in network intrusion detection with high accuracy. This study proposes a model that combines a multilayer neural network with Dense Sparse Dense (DSD) multi-stage training to simultaneously improve the criteria related to the performance of intrusion detection systems on a comprehensive dataset UNSW-NB15. We conduct experiments on many neural network models such as Recurrent Neural Network (RNN), Long-Short Term Memory (LSTM), Gated Recurrent Unit (GRU), etc. to evaluate the combined efficiency with each model through many criteria such as accuracy, detection rate, false alarm rate, precision, and F1-Score.
Characterization of directed diffusion protocol in wireless sensor networkijwmn
Wireless sensor network (WSN) has enormous applications in many places for monitoring the environments
of importance. Sensor nodes are capable of sensing, computing, and communicating. These sensor nodes
are energy constraint and operated by batteries. Since energy consumption is an important issue of WSN,
there have been many energy-efficient protocols proposed for the WSN. Directed diffusion (DD) is a datacentric
protocol that focuses on the energy efficiency of the networks. Since the first proposal of DD
protocol by Deborah, there have been various versions of DD protocols proposed by many scientists across
the globe. These upgraded versions of DD protocols add on various features to the original DD protocol
such as energy, scalability, network lifetime, security, reliability, and mobility. In this paper, we discuss
and classify various characteristics of themost populardirected diffusion protocols that have been proposed
over couple of years.
Wireless Sensor Network Based Clustering Architecture for Cooperative Communi...ijtsrd
We propose clusters based cooperatives based verbal architecture coop on the cellular ad hoc wireless sensor network Mawsn with the environment fading Rayleigh. The main ability and contributions of this paper are as follows. First, the proposed cage uses a cluster as a underlying system to help stable transmission services. 2D, the proposed enclosure uses a cluster based verbal cooperative exchange to effectively guide the package delivery ratio with multi hop power saving transmission. 0.33, we do not forget reasonable methods mainly based on cellular ad hoc nodes with sensing features and constant sensor nodes in the sensor field along with conventional research for the introduction of constant network sensors. Fourth, we have theoretical analysis with blackouts opportunities for proposed cooperative transmissions. Overall performance evaluation is run through simulation and evaluation. Sweeti Kumari | Dr. Ranjan Kumar Singh "Wireless Sensor Network Based Clustering Architecture for Cooperative Communication" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd43670.pdf Paper URL: https://www.ijtsrd.comengineering/electronics-and-communication-engineering/43670/wireless-sensor-network-based-clustering-architecture-for-cooperative-communication/sweeti-kumari
SHADOWING EFFECTS ON ROUTING PROTOCOL OF MULTIHOP AD HOC NETWORKSijasuc
Two-ray ground reflection model has been widely used as the propagation model to investigate the
performance of an ad hoc network. But two-ray model is too simple to represent a real world network. A
more realistic model namely shadowing propagation model has been used in this investigation. Under
shadowing propagation model, a mobile node may receive a packet at a signal level that is below a
required threshold level. This low signal level affects the routing protocol as well as the medium access
control protocol of a network. An analytical model has been presented in this paper to investigate the
shadowing effects on the network performance. The analytical model has been verified via simulation
results. Simulation results show that the performance of a network becomes very poor if shadowing
propagation model is used in compare to the simple two-ray model. Two solutions have also been proposed
in this paper to overcome the effects of shadowing. One solution is a physical layer solution and the other
one is a Medium Access Control (MAC) layer solution. Simulation results show that these two solutions
reduce the shadowing effect and improve network performance.
AN ENERGY EFFICIENT DISTRIBUTED PROTOCOL FOR ENSURING COVERAGE AND CONNECTIVI...ijasuc
As wireless sensor networks (WSNs) continue to attract more and more researchers attention, new ideas for
applications are continually being developed, many of which involve consistent coverage with good
network connectivity of a given area of interest. For the successful operation of the wireless Sensor
Network, the active sensor nodes must maintain both coverage and also connectivity. These are two closely
related essential prerequisites and they are also very important measurements of quality of service (QoS)
for wireless sensor networks. This paper presents the design and analysis of novel protocols that can
dynamically configure a sensor network to result in guaranteed degrees of coverage and connectivity. This
protocol is simulated using NS2 simulated and compared against a distributed probabilistic coveragepreserving configuration protocol (DPCCP) with SPAN [1] protocol in the literature and show that it
activates lesser number of sensor nodes, consumes much lesser energy and maximises the network lifetime
significantly.
Interference aware resource allocation model for D2D under cellular network IJECEIAES
Device-to-Device communication (D2D) has emerged as an efficient communication model in future generation cellular network for offloading cellular traffic and enhance overall network performance. D2D communication aid in attaining better spectrum utilization, lower delay, and less energy consumption, which can well adapt to meet demand of higher transmission rate, larger network capacity. Further, enhances spectral efficiency by reutilizing resource. However, it may result in severe cross-tier interference and co-tier interference. Therefore, efficient interference modelling design are required to address performance degradation caused by the interferences. The existing model has focused on addressing interference considering D2D association operating on same cell with the cellular association. As a result, it incurs interference to the cellular user located in the same cell. However, practically D2D association in overlapping area will reutilize spectrum of multiple neighboring cells. As a result, it incurs interference in multiple cells. For overcoming research challenges, this work presented Interference Aware Resource Allocation (IARA) model for D2D under cellular network as a game theory model. This work consider a resource allocation game where base station as a contender for catering D2D resource needs under different assumptions. Experiment are conducted to evaluate performance of IARA. The outcome shows IARA attained significant performance improvement over state-of-art models in terms of sum rate (utility), successful packet transmission, revenue, and delay.
Extending the longevity, is a significant job to be accomplished by these sensor networks. The traditional routing protocols could not be applied here, due to its nodes powered by batteries. Nodes are often clustered in to non-overlapping clusters, so as to provide energy efficiency. A concise overview on clustering processes, within wireless sensor networks is given in this paper. But it is difficult to replace the deceased batteries of the sensor nodes. A distinctive sensor node consumes much of its energy during wireless communication. This research work suggests the development of a hierarchical distributed clustering mechanism, which gives improved performance over the existing clustering algorithm LEACH. The two hiding concepts behind the proposed scheme are the hierarchical distributed clustering mechanism and the concept of threshold. Energy utilization is significantly reduced, thereby greatly prolonging the lifetime of the sensor nodes.
ON THE PERFORMANCE OF INTRUSION DETECTION SYSTEMS WITH HIDDEN MULTILAYER NEUR...IJCNCJournal
Deep learning applications, especially multilayer neural network models, result in network intrusion detection with high accuracy. This study proposes a model that combines a multilayer neural network with Dense Sparse Dense (DSD) multi-stage training to simultaneously improve the criteria related to the performance of intrusion detection systems on a comprehensive dataset UNSW-NB15. We conduct experiments on many neural network models such as Recurrent Neural Network (RNN), Long-Short Term Memory (LSTM), Gated Recurrent Unit (GRU), etc. to evaluate the combined efficiency with each model through many criteria such as accuracy, detection rate, false alarm rate, precision, and F1-Score.
Characterization of directed diffusion protocol in wireless sensor networkijwmn
Wireless sensor network (WSN) has enormous applications in many places for monitoring the environments
of importance. Sensor nodes are capable of sensing, computing, and communicating. These sensor nodes
are energy constraint and operated by batteries. Since energy consumption is an important issue of WSN,
there have been many energy-efficient protocols proposed for the WSN. Directed diffusion (DD) is a datacentric
protocol that focuses on the energy efficiency of the networks. Since the first proposal of DD
protocol by Deborah, there have been various versions of DD protocols proposed by many scientists across
the globe. These upgraded versions of DD protocols add on various features to the original DD protocol
such as energy, scalability, network lifetime, security, reliability, and mobility. In this paper, we discuss
and classify various characteristics of themost populardirected diffusion protocols that have been proposed
over couple of years.
QoS controlled capacity offload optimization in heterogeneous networksjournalBEEI
An efficient resource allocation mechanism in the physical layer of wireless networks ensures that resources such as bandwidth and power are used with high efficiency in spite of low delay and high edge user data rate. Microcells in the network are typically set with bias settings to artificially increase the Signal-to-Interference-Plus-Noise Ratio, thus encouraging users to offload to the microcell. However, the artificial bias settings are tedious and often suboptimal. This work presents a low complexity algorithm for maximization of network capacity with load balancing in a heterogeneous network without the need for bias setting. The small cells were deployed in a grid topology at a selected distance from macrocell to enhance network capacity through coverage overlap. User association and minimum user throughput were incorporated as constraints to enable closer simulation to real word Quality of Service requirements. The results showed that the proposed algorithm was able to maintain less than 10% user drop rate. The proposed algorithm can increase user confidence as well as maintain load balancing, maintain the scalability, and reduce power consumption of the wireless network.
On Demand Bandwidth Reservation for Real- Time Traffic in Cellular IP Network...IDES Editor
As real-time traffic requires more attention, it
is given priority over non-real-time traffic in Cellular IP
networks. Bandwidth reservation is often applied to serve
such traffic in order to achieve better Quality of Service
(QoS). Evolutionary Algorithms are quite useful in
solving optimization problems of such nature. This paper
employs Genetic Algorithm (GA) for bandwidth
management in Cellular IP network. It compares the
performance of the model with another model used for
optimizing Connection Dropping Probability (CDP) using
Particle Swarm Optimization (PSO). Both models, GA
based and PSO based, try to minimize the Connection
Dropping Probability for real-time users in the network
by searching the free available bandwidth in the user’s
cell or in the neighbor cells and assigning it to the realtime
users. Alternatively, if the free bandwidth is not
available, the model borrows the bandwidth from nonreal
time-users and gives it to the real-time users.
Experimental results evaluate the performance of the GA
based model. The comparative study between both the
models indicates that GA based model has an edge over
the PSO based one.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
ANALYSE THE PERFORMANCE OF MOBILE PEER TO PEER NETWORK USING ANT COLONY OPTIM...ijcsity
A mobile peer-to-peer computer network is the one in which each computer in the network can act as a
client or server for the other computers in the network. The communication process among the nodes in the
mobile peer to peer network requires more no of messages. Due to this large number of messages passing,
propose an interconnection structure called distributed Spanning Tree (DST) and it improves the efficiency
of the mobile peer to peer network. The proposed method improves the data availability and consistency
across the entire network and also reduces the data latency and the required number of message passes for
any specific application in the network. Further to enhance the effectiveness of the proposed system, the
DST network is optimized with the Ant Colony Optimization method. It gives the optimal solution of the
DST method and increased availability, enhanced consistency and scalability of the network. The
simulation results shows that reduces the number of message sent for any specific application and average
delay and increases the packet delivery ratio in the network.
PERFORMANCE COMPARISON OF QOS METRICS FOR A DISTRIBUTED PRICING SCHEMEijasuc
De-centralized nature of nodes, in ad-hoc networks, results in the users adapting their operations
independently. Such operations are mostly biased upon the figures and data available for the parameters
which are imperative for superior performance or, in other words, improved Quality of Performance (QoS)
of the nodes. In centrally controlled networks following cooperative game theory principles, collective
operations are performed by the nodes for better QoS of the network. Although nodes in decentralized
networks undertake individual operations, the final outcome of the whole network and thus the performance
of the nodes in the network are influenced by the operations of other nodes. Hence, a distributed resource
allocation approach in such a scenario can be modeled as a non-cooperative game. Asynchronous
Distributed Pricing (ADP) is one such virtual pricing algorithm in which a user’s payoff is determined by
the difference between how much a given performance metric is valued and how much is paid for it. User
service demands and priorities are modeled using numerically emulated QoS metrics termed as utility
functions. The network objective is to maximize the sum of all users’ payoff. However, for convergence of
the sum of all users’ payoff to a global maximum, the determination of the QoS metric’s utility function
with sufficient concavity is essential. Although supermodularity conditions have been previously defined
and determined to obtain suitable utility functions, we have numerically and analytically illustrated that the
convergence performance characteristics fluctuates with the choice of QoS metrics in the algorithm for
similar utility functions as well. We have assessed the optimality of utility functions under Signal-toInterference-plus-Noise ratio and Signal-to-Interference ratio based calculations. This paper also explores
into the difference in performance characteristics obtained by the addition of a significant value noise
variance in the ADP algorithm.
Simulation Issues in Wireless Sensor Networks: A SurveyM H
This paper presents a survey of simulation tools and systems for wireless sensor networks. Wireless sensor network modelling and simulation methodologies are presented for each system alongside judgments concerning their relative ease of use and accuracy. Finally, we propose a mixed-mode simulation methodology that integrates a simulated environment with real wireless sensor network testbed hardware in order to improve both the accuracy and scalability of results when evaluating different prototype designs and systems.
A STRUCTURED DEEP NEURAL NETWORK FOR DATA-DRIVEN LOCALIZATION IN HIGH FREQUEN...IJCNCJournal
Next-generation wireless networks such as 5G and 802.11ad networks will use millimeter waves operating
at 28GHz, 38GHz, or higher frequencies to deliver unprecedentedly high data rates, e.g., 10 gigabits per
second. However, millimeter waves must be used directionally with narrow beams in order to overcome the
large attenuation due to their higher frequency. To achieve high data rates in a mobile setting,
communicating nodes need to align their beams dynamically, quickly, and in high resolution. We propose a
data-driven, deep neural network (DNN) approach to provide robust localization for beam alignment,
using a lower frequency spectrum (e.g., 2.4 GHz). The proposed DNN-based localization methods use the
angle of arrival derived from phase differences in the signal received at multiple antenna arrays to infer the
location of a mobile node. Our methods differ from others that use DNNs as a black box in that the
structure of our neural network model is tailored to address difficulties associated with the domain, such as
collinearity of the mobile node with antenna arrays, fading and multipath. We show that training our
models requires a small number of sample locations, such as 30 or fewer, making the proposed methods
practical. Our specific contributions are: (1) a structured DNN approach where the neural network
topology reflects the placement of antenna arrays, (2) a simulation platform for generating training and
evaluation data sets under multiple noise models, and (3) demonstration that our structured DNN approach
improves localization under noise by up to 25% over traditional off-the-shelf DNNs, and can achieve submeter
accuracy in a real-world experiment.
OPTIMUM NEIGHBORS FOR RESOURCECONSTRAINED MOBILE AD HOC NETWORKSijasuc
This paper presents an investigation on the optimum number of neighbors for mobile ad hoc networks
(MANETs). The MANETs are self-configuring and self-organizing networks. In such a network, energyconstrained mobile nodes share limited bandwidth to send their packets to the destinations. The mobile nodes
have a limited transmission range and they rely on their neighbors to deliver their packets. Hence, the mobile
nodes must be associated with the required (i.e., optimum) number of neighbors. As the number of neighbors
is varied, a trade-off exists between the network connectivity and available bandwidth per mobile node. To
investigate this issue, we consider Dynamic Source Routing (DSR) as the routing protocol and IEEE 802.11
as the MAC layer protocol in this work. We consider both static and dynamic scenarios in this work. We
simulated the ad hoc networks via network simulator (NS-2) and the simulation results show that there exists
an optimum number of neighbors for the static case. We also show that mobility has a grave impact on the
performance of the MANETs in terms of network throughput, end-to-end delay, energy consumption, and
packet loss. Hence, we need to increase the number of neighbors under mobility conditions. However, there
is no global optimum number of neighbors for the mobility case.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A NODE DEPLOYMENT MODEL WITH VARIABLE TRANSMISSION DISTANCE FOR WIRELESS SENS...ijwmn
The deployment of network nodes is essential to ensure the wireless sensor network's regular operation and affects the multiple network performance metrics, such as connectivity, coverage, lifetime, and cost. This paper focuses on the problem of minimizing network costs while meeting network requirements, and proposes a corona-based deployment method by using the variable transmission distance sensor. Based on the analysis of node energy consumption and network cost, an optimization model to minimize Cost Per Unit Area is given. The transmission distances and initial energy of the sensors are obtained by solving the model. The optimization model is improved to ensure the energy consumption balance of nodes in the same corona. Based on these parameters, the process of network node deployment is given. Deploying the
network through this method will greatly reduce network costs.
DISTRIBUTED COVERAGE AND CONNECTIVITY PRESERVING ALGORITHM WITH SUPPORT OF DI...IJCSEIT Journal
Given a 3D space where should be supervised and a group of mobile sensor actor nodes with limited
sensing and communicating capabilities, this paper aims at proposing a distributed self-deployment
algorithm for agents to cover the space as much as possible by considering non-uniform sensing coverage
degree constraint of environment while preserving connectivity. The problem is formulated as coverage
maximization subject to connectivity and sensing coverage degree constraint. Considering a desired
distance between neighbouring nodes, an error function which depends on pairwise distance between
nodes is described. The maximization is encoded to an error minimization problem that is solved using
gradient descent algorithm and will yield in moving sensors into appropriate positions. Simulation results
are presented in two different conditions that importance of sensing coverage degree support of
environment is very high and is low.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Dear Students
Ingenious techno Solution offers an expertise guidance on you Final Year IEEE & Non- IEEE Projects on the following domain
JAVA
.NET
EMBEDDED SYSTEMS
ROBOTICS
MECHANICAL
MATLAB etc
For further details contact us:
enquiry@ingenioustech.in
044-42046028 or 8428302179.
Ingenious Techno Solution
#241/85, 4th floor
Rangarajapuram main road,
Kodambakkam (Power House)
http://www.ingenioustech.in/
Dear Students
Ingenious techno Solution offers an expertise guidance on you Final Year IEEE & Non- IEEE Projects on the following domain
JAVA
.NET
EMBEDDED SYSTEMS
ROBOTICS
MECHANICAL
MATLAB etc
For further details contact us:
enquiry@ingenioustech.in
044-42046028 or 8428302179.
Ingenious Techno Solution
#241/85, 4th floor
Rangarajapuram main road,
Kodambakkam (Power House)
http://www.ingenioustech.in/
Dear Students
Ingenious techno Solution offers an expertise guidance on you Final Year IEEE & Non- IEEE Projects on the following domain
JAVA
.NET
EMBEDDED SYSTEMS
ROBOTICS
MECHANICAL
MATLAB etc
For further details contact us:
enquiry@ingenioustech.in
044-42046028 or 8428302179.
Ingenious Techno Solution
#241/85, 4th floor
Rangarajapuram main road,
Kodambakkam (Power House)
http://www.ingenioustech.in/
Dear Students
Ingenious techno Solution offers an expertise guidance on you Final Year IEEE & Non- IEEE Projects on the following domain
JAVA
.NET
EMBEDDED SYSTEMS
ROBOTICS
MECHANICAL
MATLAB etc
For further details contact us:
enquiry@ingenioustech.in
044-42046028 or 8428302179.
Ingenious Techno Solution
#241/85, 4th floor
Rangarajapuram main road,
Kodambakkam (Power House)
http://www.ingenioustech.in/
Supporting efficient and scalable multicastingingenioustech
Dear Students
Ingenious techno Solution offers an expertise guidance on you Final Year IEEE & Non- IEEE Projects on the following domain
JAVA
.NET
EMBEDDED SYSTEMS
ROBOTICS
MECHANICAL
MATLAB etc
For further details contact us:
enquiry@ingenioustech.in
044-42046028 or 8428302179.
Ingenious Techno Solution
#241/85, 4th floor
Rangarajapuram main road,
Kodambakkam (Power House)
http://www.ingenioustech.in/
Dear Students
Ingenious techno Solution offers an expertise guidance on you Final Year IEEE & Non- IEEE Projects on the following domain
JAVA
.NET
EMBEDDED SYSTEMS
ROBOTICS
MECHANICAL
MATLAB etc
For further details contact us:
enquiry@ingenioustech.in
044-42046028 or 8428302179.
Ingenious Techno Solution
#241/85, 4th floor
Rangarajapuram main road,
Kodambakkam (Power House)
http://www.ingenioustech.in/
QoS controlled capacity offload optimization in heterogeneous networksjournalBEEI
An efficient resource allocation mechanism in the physical layer of wireless networks ensures that resources such as bandwidth and power are used with high efficiency in spite of low delay and high edge user data rate. Microcells in the network are typically set with bias settings to artificially increase the Signal-to-Interference-Plus-Noise Ratio, thus encouraging users to offload to the microcell. However, the artificial bias settings are tedious and often suboptimal. This work presents a low complexity algorithm for maximization of network capacity with load balancing in a heterogeneous network without the need for bias setting. The small cells were deployed in a grid topology at a selected distance from macrocell to enhance network capacity through coverage overlap. User association and minimum user throughput were incorporated as constraints to enable closer simulation to real word Quality of Service requirements. The results showed that the proposed algorithm was able to maintain less than 10% user drop rate. The proposed algorithm can increase user confidence as well as maintain load balancing, maintain the scalability, and reduce power consumption of the wireless network.
On Demand Bandwidth Reservation for Real- Time Traffic in Cellular IP Network...IDES Editor
As real-time traffic requires more attention, it
is given priority over non-real-time traffic in Cellular IP
networks. Bandwidth reservation is often applied to serve
such traffic in order to achieve better Quality of Service
(QoS). Evolutionary Algorithms are quite useful in
solving optimization problems of such nature. This paper
employs Genetic Algorithm (GA) for bandwidth
management in Cellular IP network. It compares the
performance of the model with another model used for
optimizing Connection Dropping Probability (CDP) using
Particle Swarm Optimization (PSO). Both models, GA
based and PSO based, try to minimize the Connection
Dropping Probability for real-time users in the network
by searching the free available bandwidth in the user’s
cell or in the neighbor cells and assigning it to the realtime
users. Alternatively, if the free bandwidth is not
available, the model borrows the bandwidth from nonreal
time-users and gives it to the real-time users.
Experimental results evaluate the performance of the GA
based model. The comparative study between both the
models indicates that GA based model has an edge over
the PSO based one.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
ANALYSE THE PERFORMANCE OF MOBILE PEER TO PEER NETWORK USING ANT COLONY OPTIM...ijcsity
A mobile peer-to-peer computer network is the one in which each computer in the network can act as a
client or server for the other computers in the network. The communication process among the nodes in the
mobile peer to peer network requires more no of messages. Due to this large number of messages passing,
propose an interconnection structure called distributed Spanning Tree (DST) and it improves the efficiency
of the mobile peer to peer network. The proposed method improves the data availability and consistency
across the entire network and also reduces the data latency and the required number of message passes for
any specific application in the network. Further to enhance the effectiveness of the proposed system, the
DST network is optimized with the Ant Colony Optimization method. It gives the optimal solution of the
DST method and increased availability, enhanced consistency and scalability of the network. The
simulation results shows that reduces the number of message sent for any specific application and average
delay and increases the packet delivery ratio in the network.
PERFORMANCE COMPARISON OF QOS METRICS FOR A DISTRIBUTED PRICING SCHEMEijasuc
De-centralized nature of nodes, in ad-hoc networks, results in the users adapting their operations
independently. Such operations are mostly biased upon the figures and data available for the parameters
which are imperative for superior performance or, in other words, improved Quality of Performance (QoS)
of the nodes. In centrally controlled networks following cooperative game theory principles, collective
operations are performed by the nodes for better QoS of the network. Although nodes in decentralized
networks undertake individual operations, the final outcome of the whole network and thus the performance
of the nodes in the network are influenced by the operations of other nodes. Hence, a distributed resource
allocation approach in such a scenario can be modeled as a non-cooperative game. Asynchronous
Distributed Pricing (ADP) is one such virtual pricing algorithm in which a user’s payoff is determined by
the difference between how much a given performance metric is valued and how much is paid for it. User
service demands and priorities are modeled using numerically emulated QoS metrics termed as utility
functions. The network objective is to maximize the sum of all users’ payoff. However, for convergence of
the sum of all users’ payoff to a global maximum, the determination of the QoS metric’s utility function
with sufficient concavity is essential. Although supermodularity conditions have been previously defined
and determined to obtain suitable utility functions, we have numerically and analytically illustrated that the
convergence performance characteristics fluctuates with the choice of QoS metrics in the algorithm for
similar utility functions as well. We have assessed the optimality of utility functions under Signal-toInterference-plus-Noise ratio and Signal-to-Interference ratio based calculations. This paper also explores
into the difference in performance characteristics obtained by the addition of a significant value noise
variance in the ADP algorithm.
Simulation Issues in Wireless Sensor Networks: A SurveyM H
This paper presents a survey of simulation tools and systems for wireless sensor networks. Wireless sensor network modelling and simulation methodologies are presented for each system alongside judgments concerning their relative ease of use and accuracy. Finally, we propose a mixed-mode simulation methodology that integrates a simulated environment with real wireless sensor network testbed hardware in order to improve both the accuracy and scalability of results when evaluating different prototype designs and systems.
A STRUCTURED DEEP NEURAL NETWORK FOR DATA-DRIVEN LOCALIZATION IN HIGH FREQUEN...IJCNCJournal
Next-generation wireless networks such as 5G and 802.11ad networks will use millimeter waves operating
at 28GHz, 38GHz, or higher frequencies to deliver unprecedentedly high data rates, e.g., 10 gigabits per
second. However, millimeter waves must be used directionally with narrow beams in order to overcome the
large attenuation due to their higher frequency. To achieve high data rates in a mobile setting,
communicating nodes need to align their beams dynamically, quickly, and in high resolution. We propose a
data-driven, deep neural network (DNN) approach to provide robust localization for beam alignment,
using a lower frequency spectrum (e.g., 2.4 GHz). The proposed DNN-based localization methods use the
angle of arrival derived from phase differences in the signal received at multiple antenna arrays to infer the
location of a mobile node. Our methods differ from others that use DNNs as a black box in that the
structure of our neural network model is tailored to address difficulties associated with the domain, such as
collinearity of the mobile node with antenna arrays, fading and multipath. We show that training our
models requires a small number of sample locations, such as 30 or fewer, making the proposed methods
practical. Our specific contributions are: (1) a structured DNN approach where the neural network
topology reflects the placement of antenna arrays, (2) a simulation platform for generating training and
evaluation data sets under multiple noise models, and (3) demonstration that our structured DNN approach
improves localization under noise by up to 25% over traditional off-the-shelf DNNs, and can achieve submeter
accuracy in a real-world experiment.
OPTIMUM NEIGHBORS FOR RESOURCECONSTRAINED MOBILE AD HOC NETWORKSijasuc
This paper presents an investigation on the optimum number of neighbors for mobile ad hoc networks
(MANETs). The MANETs are self-configuring and self-organizing networks. In such a network, energyconstrained mobile nodes share limited bandwidth to send their packets to the destinations. The mobile nodes
have a limited transmission range and they rely on their neighbors to deliver their packets. Hence, the mobile
nodes must be associated with the required (i.e., optimum) number of neighbors. As the number of neighbors
is varied, a trade-off exists between the network connectivity and available bandwidth per mobile node. To
investigate this issue, we consider Dynamic Source Routing (DSR) as the routing protocol and IEEE 802.11
as the MAC layer protocol in this work. We consider both static and dynamic scenarios in this work. We
simulated the ad hoc networks via network simulator (NS-2) and the simulation results show that there exists
an optimum number of neighbors for the static case. We also show that mobility has a grave impact on the
performance of the MANETs in terms of network throughput, end-to-end delay, energy consumption, and
packet loss. Hence, we need to increase the number of neighbors under mobility conditions. However, there
is no global optimum number of neighbors for the mobility case.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A NODE DEPLOYMENT MODEL WITH VARIABLE TRANSMISSION DISTANCE FOR WIRELESS SENS...ijwmn
The deployment of network nodes is essential to ensure the wireless sensor network's regular operation and affects the multiple network performance metrics, such as connectivity, coverage, lifetime, and cost. This paper focuses on the problem of minimizing network costs while meeting network requirements, and proposes a corona-based deployment method by using the variable transmission distance sensor. Based on the analysis of node energy consumption and network cost, an optimization model to minimize Cost Per Unit Area is given. The transmission distances and initial energy of the sensors are obtained by solving the model. The optimization model is improved to ensure the energy consumption balance of nodes in the same corona. Based on these parameters, the process of network node deployment is given. Deploying the
network through this method will greatly reduce network costs.
DISTRIBUTED COVERAGE AND CONNECTIVITY PRESERVING ALGORITHM WITH SUPPORT OF DI...IJCSEIT Journal
Given a 3D space where should be supervised and a group of mobile sensor actor nodes with limited
sensing and communicating capabilities, this paper aims at proposing a distributed self-deployment
algorithm for agents to cover the space as much as possible by considering non-uniform sensing coverage
degree constraint of environment while preserving connectivity. The problem is formulated as coverage
maximization subject to connectivity and sensing coverage degree constraint. Considering a desired
distance between neighbouring nodes, an error function which depends on pairwise distance between
nodes is described. The maximization is encoded to an error minimization problem that is solved using
gradient descent algorithm and will yield in moving sensors into appropriate positions. Simulation results
are presented in two different conditions that importance of sensing coverage degree support of
environment is very high and is low.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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Supporting efficient and scalable multicastingingenioustech
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SHADOWING EFFECTS ON ROUTING PROTOCOL OF MULTIHOP AD HOC NETWORKSijasuc
Two-ray ground reflection model has been widely used as the propagation model to investigate the
performance of an ad hoc network. But two-ray model is too simple to represent a real world network. A
more realistic model namely shadowing propagation model has been used in this investigation. Under
shadowing propagation model, a mobile node may receive a packet at a signal level that is below a
required threshold level. This low signal level affects the routing protocol as well as the medium access
control protocol of a network. An analytical model has been presented in this paper to investigate the
shadowing effects on the network performance. The analytical model has been verified via simulation
results. Simulation results show that the performance of a network becomes very poor if shadowing
propagation model is used in compare to the simple two-ray model. Two solutions have also been proposed
in this paper to overcome the effects of shadowing. One solution is a physical layer solution and the other
one is a Medium Access Control (MAC) layer solution. Simulation results show that these two solutions
reduce the shadowing effect and improve network performance.
SHADOWING EFFECTS ON ROUTING PROTOCOL OF MULTIHOP AD HOC NETWORKSijasuc
Two-ray ground reflection model has been widely used as the propagation model to investigate the
performance of an ad hoc network. But two-ray model is too simple to represent a real world network. A
more realistic model namely shadowing propagation model has been used in this investigation. Under
shadowing propagation model, a mobile node may receive a packet at a signal level that is below a
required threshold level. This low signal level affects the routing protocol as well as the medium access
control protocol of a network. An analytical model has been presented in this paper to investigate the
shadowing effects on the network performance. The analytical model has been verified via simulation
results. Simulation results show that the performance of a network becomes very poor if shadowing
propagation model is used in compare to the simple two-ray model. Two solutions have also been proposed
in this paper to overcome the effects of shadowing. One solution is a physical layer solution and the other
one is a Medium Access Control (MAC) layer solution. Simulation results show that these two solutions
reduce the shadowing effect and improve network performance.
An Efficient Approach for Data Gathering and Sharing with Inter Node Communi...cscpconf
In today’s era Wireless sensor networks (WSNs) have emerged as a solution for a wide range of
applications. Most of the traditional WSN architectures consist of static nodes which are densely deployed
over a sensing area. Recently, several WSN architectures based on mobile elements (MEs) have been
proposed. Most of them exploit mobility to address the problem of data collection in WSNs. The common
drawback among them is to data sharing between interconnected nodes. In this paper we propose an
Efficient Approach for Data Gathering and Sharing with Inter Node Communication in Mobile-Sink. Our
algorithm is divided into seven parts: Registration Phase, Authentication Phase, Request and Reply Phase,
Setup Phase, Setup Phase (NN), Data Gathering, and Forwarding to Sink. Our approach provides an
efficient way to handle data in between the intercommunication nodes. By the above approach we can
access the data from the node which is not in the list, by sharing the data from the node which is
approachable to the desired node. For accessing and sharing we need some security so that the data can
be shared between authenticated nodes. For this we use two way security approach one for the accessing
node and other for the sharing.
LIFETIME IMPROVEMENT USING MOBILE AGENT IN WIRELESS SENSOR NETWORKJournal For Research
Wireless sensor networks have attracted much attention in the research community over the last few years, driven by a wealth of theoretical and practical challenges and an increasing number of practical civilian application. ‘one deployment, multiple applications’ is an emerging trend in the development of WSN, due to the high cost of deploying hundreds and thousands of sensors nodes over a wide geographical area and the application-specific nature of tasking a WSN. A wireless sensor network is a collection of nodes organized into a cooperative network. To reduce the energy consumption, the transmission of data between sensor nodes must be reduced in order to preserve the remaining energy in cluster node. We propose a new energy balancing architecture based on cluster with hexagonal geometry with radius R.select the base station and after select the cluster head with maximum energy of the node and after select mobile agent in minimum distance to cluster head and second highest maximum energy. And then send the data mobile agent to cluster head and cluster head to base station.and we have energy management must be followed to balance the energy in the whole network and improving network lifetime.
DATA TRANSMISSION IN WIRELESS SENSOR NETWORKS FOR EFFECTIVE AND SECURE COMMUN...IJEEE
Data transmission occurs from transmitting node to sink node, which communicate each other via large number of intermediate nodes or directly to an external base station. A network consists of numbers of nodes with one as a source and one or more as a destination node.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Optimum Neighbors for Resource-Constrained Mobile Ad Hoc Networksijasuc
This paper presents an investigation on the optimum number of neighbors for mobile ad hoc networks
(MANETs). The MANETs are self-configuring and self-organizing networks. In such a network, energyconstrained mobile nodes share limited bandwidth to send their packets to the destinations. The mobile nodes
have a limited transmission range and they rely on their neighbors to deliver their packets. Hence, the mobile
nodes must be associated with the required (i.e., optimum) number of neighbors. As the number of neighbors
is varied, a trade-off exists between the network connectivity and available bandwidth per mobile node. To
investigate this issue, we consider Dynamic Source Routing (DSR) as the routing protocol and IEEE 802.11
as the MAC layer protocol in this work. We consider both static and dynamic scenarios in this work. We
simulated the ad hoc networks via network simulator (NS-2) and the simulation results show that there exists
an optimum number of neighbors for the static case. We also show that mobility has a grave impact on the
performance of the MANETs in terms of network throughput, end-to-end delay, energy consumption, and
packet loss. Hence, we need to increase the number of neighbors under mobility conditions. However, there
is no global optimum number of neighbors for the mobility case.
OPTIMUM NEIGHBORS FOR RESOURCECONSTRAINED MOBILE AD HOC NETWORKSijasuc
Wireless networking has been an active research focus since the early days of the packet radio
network introduced by the Defense Advanced Research Project Agency (DARPA) [1]. Recent
developments in wireless devices have made laptop computers, personal digital assistants (PDA),
pagers, and cellular telephones portable. Now, users can carry these devices to any place at any
time. Hence, there is a need for a network that can be deployed at any place at any time without
any infrastructure support. In some cases, an infrastructure-based network is hard to build.
Networks used by the soldiers on the battlefield are worthwhile to mention here. In some cases,
infrastructures may not exist due to natural calamities such as cyclones, tsunami, and tornados.
Hence, there is always a need for setting up a temporary network among a group of users without
any pre-existing infrastructure and centralized administration. Mobile Ad hoc Networks
(MANETs) are considered suitable solutions for these kinds of temporary networks. MANETs
consist of a group of mobile nodes, which have limited battery and limited processing power.
MANETs are self-organizing and self-configuring networks and they can be deployed without any
infrastructure support. Numerous groundbreaking applications have been proposed based on
MANETs. These applications include disaster management, search and recovery, remote
International Journal of Ad hoc, Sensor & Ubiquitous Computing (IJASUC) Vol.12, No.2, April 2021
2
healthcare, tele-geoprocessing, education, traffic management, process control, and security [2].
These applications impose diversified design and performance constraints on the MANETs.
OPTIMUM NEIGHBORS FOR RESOURCECONSTRAINED MOBILE AD HOC NETWORKSijasuc
This paper presents an investigation on the optimum number of neighbors for mobile ad hoc networks
(MANETs). The MANETs are self-configuring and self-organizing networks. In such a network, energyconstrained mobile nodes share limited bandwidth to send their packets to the destinations. The mobile nodes
have a limited transmission range and they rely on their neighbors to deliver their packets. Hence, the mobile
nodes must be associated with the required (i.e., optimum) number of neighbors. As the number of neighbors
is varied, a trade-off exists between the network connectivity and available bandwidth per mobile node. To
investigate this issue, we consider Dynamic Source Routing (DSR) as the routing protocol and IEEE 802.11
as the MAC layer protocol in this work. We consider both static and dynamic scenarios in this work. We
simulated the ad hoc networks via network simulator (NS-2) and the simulation results show that there exists
an optimum number of neighbors for the static case. We also show that mobility has a grave impact on the
performance of the MANETs in terms of network throughput, end-to-end delay, energy consumption, and
packet loss. Hence, we need to increase the number of neighbors under mobility conditions. However, there
is no global optimum number of neighbors for the mobility case.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
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A Fuzzy Based Priority Approach in Mobile Sensor Network CoverageIDES Editor
In this paper a new fuzzy based approach for
improving network coverage in wireless mobile sensor
networks is proposed. In the proposed approach firstly
each mobile sensor node determines its neighbors and its
distance from borders and obstacles. According to these
values, fuzzy inference engine calculates the priority of
node for movement. Then according to the priority, in
turn, nodes move away from each other to increase
coverage area in the target field. Simulation results show
that our fuzzy approach can reach higher degree of
coverage against other common approaches like FOA,
VEC and TRI algorithms.
Wideband Sensing for Cognitive Radio Systems in Heterogeneous Next Generation...CSCJournals
Mobile Next Generation Network (MNGN) is characterized as heterogeneous network where variety of access technologies are meant to coexist. Decisions on choosing an air interface that meets a particular need at a particular time will be shifted from the network’s side to (a more intelligent) user’s side. On top of that network operators and regularities have come to the realization that assigned spectrum bands are not utilized as they should be. Cognitive radio stands out as a candidate technology to address many emerging issues in MNGN such as capacity, quality of service and spectral efficiency. As a transmission strategy, cognitive radio systems depend greatly on sensing the radio environment. In this paper, we present a novel approach for interference characterization in cognitive radio networks based on wideband chirp signal. The results presented show that improved sensing accuracy is maintained at tolerable system complexity.
Scheduling different types of packets, such as
real-time and non-real-time data packets, at sensor nodes with
resource constraints in Wireless Sensor Networks (WSN) is of
vital importance to reduce sensors’ energy consumptions and endto-end
data transmission delays. Most of the existing packetscheduling
mechanisms of WSN use First Come First Served
(FCFS), non pre-emptive priority and pre-emptive priority
scheduling algorithms. These algorithms incur a high processing
overhead and long end-to-end data transmission delay due to the
FCFS concept, starvation of high priority real-time data packets
due to the transmission of a large data packet in non pre-emptive
priority scheduling, starvation of non-real-time data packets due
to the probable continuous arrival of real-time data in preemptive
priority scheduling, and improper allocation of data
packets to queues in multilevel queue scheduling algorithms.
Moreover, these algorithms are not dynamic to the changing
requirements of WSN applications since their scheduling policies
are predetermined.
In the Advanced Multilevel Priority packet scheduling
scheme, each node except those at the last level has three levels of
priority queues. According to the priority of the packet and
availability of the queue, node will schedule the packet for
transmission. Due to separated queue availability, packet
transmission delay is reduced. Due to reduction in packet
transmission delay, node can goes into sleep mode as soon as
possible. And Expired packets are deleted at the particular node
at itself before reaching the base station, so that processing
burden on the node is reduced. Thus, energy of the node is saved.
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On the quality of service of crash recoveryingenioustech
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A dynamic performance-based_flow_controlingenioustech
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
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Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
Biological screening of herbal drugs: Introduction and Need for
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Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
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This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
1. 1
Throughput Optimization in
Mobile Backbone Networks
Emily M. Craparo, Member, IEEE, Jonathan P. How, Senior Member, IEEE,
and Eytan Modiano, Senior Member, IEEE
Abstract—This paper describes new algorithms for throughput optimization in a mobile backbone network. This hierarchical
communication framework combines mobile backbone nodes, which have superior mobility and communication capability, with
regular nodes, which are constrained in mobility and communication capability. An important quantity of interest in mobile backbone
networks is the number of regular nodes that can be successfully assigned to mobile backbone nodes at a given throughput level.
This paper develops a novel technique for maximizing this quantity in networks of fixed regular nodes using mixed-integer linear
programming (MILP). The MILP-based algorithm provides a significant reduction in computation time compared to existing methods
and is computationally tractable for problems of moderate size. An approximation algorithm is also developed that is appropriate for
large-scale problems. This paper presents a theoretical performance guarantee for the approximation algorithm and also demonstrates
its empirical performance. Finally, the mobile backbone network problem is extended to include mobile regular nodes, and exact and
approximate solution algorithms are presented for this extension.
Index Terms—Wireless sensor networks, mobile communication systems.
!
1 I NTRODUCTION not been adequately addressed. This paper provides tractable
solutions to the important problem of maximizing the number
D ETECTION and monitoring of spatially distributed phe-
nomena often necessitates the distribution of sensing
platforms. For example, multiple mobile robots can be used to
of regular nodes that achieve a desired level of throughput. It
also describes a new mobile backbone network optimization
problem formulation that models regular node mobility, and
explore an area of interest more rapidly than a single mobile
it provides tractable solutions to this problem, including the
robot [1], and multiple sensors can provide simultaneous
first known approximation algorithm with computation time
coverage of a relatively large area for an extended period of
that is polynomial in both the number of regular nodes and
time [2]. However, in many applications the data collected by
the number of mobile backbone nodes.
these distributed platforms is best utilized after it has been
aggregated, which requires communication among the robotic 2 BACKGROUND AND P ROBLEM S TATEMENT
or sensing agents. This paper focuses on a hierarchical network
architecture called a mobile backbone network, in which mo- Mobile backbone networks were described by Rubin et al.
bile agents are deployed to provide long-term communication [4] and Xu et al. [5] as a solution to the scalability issues
support for other agents in the form of a fixed backbone over inherent in mobile ad hoc networks. Noting that most commu-
which end-to-end communication can take place. Mobile back- nication bandwidth in single-layer large-scale mobile networks
bone networks can be used to model a variety of multi-agent is dedicated to packet-forwarding and routing overhead, they
systems. For example, a heterogeneous system composed of proposed a multi-layer hierarchical network architecture, as is
air and ground vehicles conducting ground measurements in currently used in the Internet. Srinivas et al. [6] defined two
a cluttered environment can be appropriately modeled as a types of nodes: regular nodes, which have limited mobility and
mobile backbone network, as can a team of mobile robotic communication capability, and mobile backbone nodes, which
agents deployed to collect streams of data from a network of have greater communication capability than regular nodes and
stationary sensor nodes. which can be placed at arbitrary locations in order to provide
communication support for the regular nodes.
Previous work has focused on optimal placement of mobile
Srinivas et al. [6] formulated the connected disk cover
backbone nodes in networks of fixed regular nodes, with the
(CDC) problem, in which many mobile backbone nodes with
objective of providing permanent communication support
fixed communication ranges are deployed to provide commu-
for the regular nodes [3]. Existing techniques, while exact,
nication support for a set of fixed regular nodes. The goal of
suffer from intractable computation times, even for problems
the CDC problem is to place the minimum number of mobile
of modest size. Furthermore, mobility of regular nodes has
backbone nodes such that each regular node is covered by
at least one mobile backbone node and all mobile backbone
• E. M. Craparo, J. P. How and E. Modiano are with the Department
of Aeronautics and Astronautics, Massachusetts Institute of Technology,
nodes are connected to each other. Thus, the CDC problem
Cambridge, MA 02139. takes a discrete approach to modeling communication, in that
E-mail: emilyc@alum.mit.edu two nodes can communicate if they are within communication
range of each other, and otherwise cannot.
2. 2
This paper uses a more sophisticated model of communi- for the mobile backbone nodes to be “connected” to one
cation similar to that described by Srinivas and Modiano [3]. another. This assumption models the case in which mobile
We assume that the throughput (data rate) that can be achieved backbone nodes serve to provide a satellite uplink for regular
between a regular node and a mobile backbone node is a nodes; this is the case, for instance, in hastily-formed networks
monotonically nonincreasing function of both the distance that operate in disaster areas [7]. This assumption is also
between the two nodes and the number of other regular valid for the case in which the mobile backbone nodes are
nodes that are also communicating with that particular mobile known to be powerful enough to communicate effectively over
backbone node and thus causing interference. While our results the entire problem domain. For cases in which the problem
are valid for any throughput function that is monotonically domain is so large that mobile backbone nodes have difficulty
nonincreasing in both distance and cluster size, it is useful communicating with each other, it would be necessary to
to gain intuition by considering a particular example. One develop algorithms to ensure connectivity between the mobile
such example is the throughput function resulting from the backbone nodes (see [6], for example).
use of a Slotted Aloha communication protocol in which all We seek to provide the best possible throughput on a
regular nodes are equally likely to transmit. In this protocol, permanent basis; therefore, once the mobile backbone nodes
the throughput τ between regular node i and mobile backbone have been placed at their optimal positions, no improvement
node j is given by can be obtained by moving further. Thus, our model represents
1 1 (|A j |−1) 1 a “one-time” network design problem and is also suitable
τ(A j , di j ) = (1 − ) ( α ), (1) for cases in which mobile backbone nodes are deployable,
Aj Aj di j
but cannot move once they have been deployed. This is in
where A j is the number of regular nodes assigned to mobile contrast to the message ferrying problem, in which regular
backbone node j, di j is the distance between regular node i nodes have a finite amount of data available to transmit, and
and mobile backbone node j, and α is the path loss exponent. mobile backbone nodes must move around the network and
As noted in Ref. [3], one can use the fact that collect data [8]-[11].
1 1 We assume that the positions of regular nodes are known
(1 − )c−1 ≈ with complete accuracy, e.g., because the regular nodes are
c e
equipped with GPS. The problem of dealing with error in
for c > 0 to obtain a simpler expression for the Slotted regular node position estimates is a topic of future research.
Aloha throughput function. In this simplified expression, the As posed, the mobile backbone network optimization prob-
throughput is given by lem is quite difficult. Consider a simplification in which the
1 problem is decomposed into two parts: mobile backbone node
τ(A j , di j ) ≈ (2) placement and regular node assignment. Because the mobile
e · A j · diαj
backbone nodes can be placed anywhere in the plane, the
where e is the base of the natural logarithm. problem of finding an optimal placement is a hard nonconvex
Building upon this continuous throughput model, we pose optimization problem even when a simple heuristic technique
the mobile backbone network optimization problem as follows: is used to solve the assignment portion of the problem.
given a set of N regular nodes distributed in a plane, our Similarly, given a placement of mobile backbone nodes, the
goal is to place K mobile backbone nodes, which can occupy assignment portion of the problem is also non-trivial. An
arbitrary locations in the plane, while simultaneously assigning exhaustive enumeration of all K N possible assignments is
the regular nodes to the mobile backbone nodes, such that the impractical, and naive assignment techniques, such as that of
effectiveness of the resulting network is maximized. In this assigning each regular node to the nearest mobile backbone
work, the effectiveness of the resulting network is measured node, can perform quite badly [3].
by the number of regular nodes that achieve throughput at Although the problem considered in this paper is similar
least τmin , although other formulations (such as that which to that encountered in cellular network optimization, the
maximizes the aggregate throughput achieved by all regular approaches taken herein differ from those in the cellular liter-
nodes) are possible. The particular choice of objective in this ature. Some approaches to cellular network optimization take
work is motivated by applications such as control over a base station placement to be given, then optimize over user
network, in which a minimum throughput level is required, assignment and transmission power to minimize total overall
or sensing applications in which sensor measurements are of interference [12]-[15]. Others assume a simple heuristic for
a particular (known) size. Thus, our objective is to maximize the assignment subproblem and proceed to choose base station
the number of regular nodes that achieve throughput at least locations from among a restricted set [16], [17]. In contrast,
τmin . we seek to optimize the network simultaneously over mobile
Each regular node can be assigned to a single mobile backbone node placement and regular node assignment, with-
backbone node, and it is assumed that regular nodes assigned out assuming variable transmission power capability on the
to one mobile backbone node encounter no interference from part of the regular nodes and without limiting the placement
regular nodes assigned to other mobile backbone nodes (e.g., of the mobile backbone nodes.
because each “cluster” composed of a mobile backbone node A typical example of an optimal solution to the simultane-
and its assigned regular nodes operates at a different frequency ous placement and assignment problem is shown in Fig. 1 for
than other clusters). We also assume that there is no need a group of regular nodes denoted by ◦. The mobile backbone
3. 3
where A is the set of valid assignments (i.e., those in which
each regular node is assigned to at most one mobile backbone
node), and Fτ (R, M, A, τmin ) is the number of regular nodes
that achieve throughput level τmin , given node placements R
and M, assignment A, and throughput function τ.
As discussed in Section 2, this problem is quite difficult.
Fortunately, it is possible to solve a simpler problem that
nonetheless yields an optimal solution to the original problem.
A key insight discussed in Refs. [3], [18] is that although
the mobile backbone nodes can occupy arbitrary locations,
they can be restricted to a small number of locations without
sacrificing optimality. For throughput functions that are mono-
tonically nonincreasing in distance, each mobile backbone
node can be placed at the 1-center of its assigned regular
nodes in an optimal solution.
The 1-center location for a set of regular nodes is the
Fig. 1. A typical example of an optimal mobile backbone location that minimizes the maximum distance from the mo-
network. Mobile backbone nodes, indicated by ∗, are bile backbone node to any of the regular nodes in the set.
placed such that they provide communication support for Consider a feasible solution to the mobile backbone network
regular nodes, shown as ◦. Each regular node is assigned optimization problem, i.e., a solution in which K mobile
to one mobile backbone node. Dashed lines indicate the backbone nodes are placed anywhere in the plane, each regular
radius of each cluster of nodes. node is assigned to at most one mobile backbone node, and
nodes, denoted by ∗, have been placed, and regular nodes have each assigned regular node achieves throughput at least τmin .
been assigned to them such that the number of regular nodes Let Ak denote the set of regular nodes assigned to mobile
that achieve throughput τmin is maximized. This example is backbone node k, for k = 1, ..., K, and let rk denote the distance
typical of an optimal solution in that the clusters of regular from mobile backbone node k to the most distant regular node
nodes and mobile backbone nodes are of relatively small in Ak . By our assumption that the solution is feasible, we
size, and the regular nodes are distributed intelligently among know that τ(|Ak |, rk ) ≥ τmin . Now, modify the solution such
the mobile backbone nodes, with fewer regular nodes being that mobile backbone node k is placed at the 1-center of the
allocated to mobile backbone nodes with larger cluster radii. In set Ak , leaving the assignment Ak unchanged. By definition
this example, all regular nodes have been successfully assigned of the 1-center, the distance from every regular node in Ak
to mobile backbone nodes. to mobile backbone node k is no more than rk . In particular,
In the problem considered in Figure 1, regular nodes are if the distance from the mobile backbone node to the most
stationary, and their positions are given as problem data, as distant regular node in Ak is now denoted by rk , we know
has been assumed in previous work [3]. New solutions to that τ(|Ak |, rk ) ≥ τ(|Ak |, rk ) ≥ τmin , since τ is a nonincreasing
this problem are described in Section 3. In Section 4, we function of distance. Thus, the modified solution in which the
consider an extension to this problem in which the placement mobile backbone node is placed at the 1-center of its assigned
of regular nodes is also a decision variable. That is, the goal regular nodes is feasible and has the same objective value as
in Section 4 is to place both N regular nodes and K mobile the original solution. Repeating the argument for the remaining
backbone nodes, while simultaneously assigning regular nodes mobile backbone nodes 1, ..., K, we can see that restricting the
to mobile backbone nodes, such that the effectiveness of the feasible set of mobile backbone node locations to the set of 1-
overall network is maximized. center locations of all subsets of regular nodes does not reduce
the maximum objective value that can be obtained.
Fortunately, although there are 2N possible subsets of N
3 S TATIONARY REGULAR NODES
regular nodes, there are only O(N 3 ) distinct 1-center lo-
This section describes the mobile backbone network optimiza- cations [19]. Although a particular 1-center location may
tion problem in which regular nodes are stationary. Denoting correspond to multiple subsets of regular nodes, it is uniquely
the problem data as Ri (the locations of the regular nodes, defined by the regular nodes that are most distant from it
i = 1, . . . , N), τmin (the desired minimum throughput level), in all of these sets. Each 1-center location either coincides
and τ (the throughput function); and the decision variables with a regular node, lies at the center of the diameter de-
as Mi (the selected locations of the mobile backbone nodes, scribed by two regular nodes, or lies at the circumcenter of
i = 1, . . . , K), and A (the assignment of regular nodes to mobile N
three regular nodes [20]. Thus, there are at most +
backbone nodes), this optimization problem can be stated as: 1
N N
max Fτ (R, M, A, τmin ) + distinct 1-center locations, and they can be
M, A 2 3
efficiently enumerated through enumeration of the possible
subject to Mi ∈ R2 , i = 1, . . . , K
sets of “defining” regular nodes. Moreover, the maximum
A∈A communication radius associated with each possible mobile
4. 4
N+1
backbone node location is easy to compute. This radius, which
1
we will denote as the 1-center radius, is the distance from N+2
the 1-center location to any of the defining regular nodes. y1c1
2
For 1-center locations defined by the diameter between two N+3
y2c2
nodes or the circumcircle of three nodes, the 1-center radius
y3c3
…
is simply the radius of the associated circle. For 1-center
…
t
locations defined by a single regular node, the associated 1- s
i yjcj
center radius is zero.1 N+j
The insight that mobile backbone nodes can be restricted
…
to a relatively small number of locations without sacrificing yMcM
…
optimality of the overall solution allows the mobile backbone
N
network optimization problem to be simplified. The problem
N+M
becomes
max Fτ (R, M, A, τmin ) Fig. 2. The network design problem corresponding to
M, A
the joint placement and assignment problem for mobile
subject to Mi ∈ C(R), i = 1, . . . , K backbone networks. Unlabeled arc capacities are equal
A∈A to one.
where C(R) denotes the set of 1-center locations of the regular
nodes, and |C| = O(N 3 ).
Slotted Aloha function described by Eq. (2), one can simply
take the inverse of the expression with respect to cluster size,
3.1 MILP approach
evaluate the inverse at the desired minimum throughput level
A primary contribution of this work is the development of τmin , and take the floor of the result to obtain an integer value
a single optimization problem that simultaneously solves the for ci . For the throughput function given by Eq. (2), we have
mobile backbone node placement and regular node assignment
1
problems. This is accomplished through the formulation of a ci = , (3)
network design problem. In network design problems, a given e · τmin · riα
network (represented by a directed graph) can be augmented where ri is the 1-center radius associated with 1-center location
with additional arcs for a given cost, and the goal is to i. If the throughput function cannot easily be inverted with re-
intelligently “purchase” a subset of these arcs in order to spect to cluster size, as is the case with the exact Slotted Aloha
achieve a desired flow characteristic [21]. throughput function given in Eq. (1), one can perform a search
The network design problem that produces an optimal for the largest cluster size ci ≤ N such that τ(ci , ri ) ≥ τmin .
solution to the mobile backbone network optimization problem For example, a binary search for ci would involve O(log(N))
is constructed as follows. A source node, s, is connected to evaluations of the function τ. In either case, the resulting value
each node in the set of nodes N= {1, . . . , N} (see Fig. 2). of ci is the maximum number of regular nodes that can be
N represents the set of regular nodes. The arcs connecting assigned to the mobile backbone node at location i, such that
s to i ∈ N are of unit capacity. Each node i ∈ N is in turn each of these regular nodes achieves throughput at least τmin .
connected to a subset of the nodes in M= {N + 1, . . . , N + M}, Denote the set of nodes for the network design problem
where M is O(N 3 ). M represents the set of possible mobile by N and the set of arcs by A . If K mobile backbone
backbone node locations, i.e., the 1-center locations of the nodes are available to provide communication support for N
subsets of regular nodes. Node i ∈ N is connected to node regular nodes at given locations, and a throughput level τmin is
N + j ∈ M if, and only if, regular node i is within the 1-center specified, the goal of the network design problem is to select
radius of location j. The arc connecting i to N + j is of unit K arcs incident to the sink and a feasible flow x such that the
capacity. Finally, each node in M is connected to the sink, net flow through the graph is maximized.
t. The capacity of the arc connecting node N + i ∈ M to the The network design problem can be solved via the following
sink is the product of a binary variable yi , which represents mixed-integer linear program (MILP), which we denote as the
the decision of whether to place a mobile backbone node at
Network Design MILP:
location i, and a constant ci , which is the maximum number of
N
regular nodes that can be assigned to a mobile backbone node
max ∑ xsi (4a)
at location i at the desired throughput level τmin . The quantity x,y
i=1
ci can be efficiently computed in one of two ways. For an M
easily-inverted throughput function such as the approximate subject to ∑ yi = K (4b)
i=1
1. In practice, we consider the 1-center radius of such locations to have
a small positive value ε in order to assure boundedness of the throughput ∑ xi j = ∑ xli i ∈ N {s,t} (4c)
function; this modification does not impact the solution as long as ε is such j:(i, j)∈A l:(l,i)∈A
that the throughput achieved by the regular node does not cross the threshold xi j ≥ 0 ∀ (i, j) ∈ A (4d)
of τmin , and no additional regular nodes fall within a distance of ε of the
mobile backbone node. xi j ≤ 1 ∀ (i, j) ∈ A : j ∈ N {t} (4e)
5. 5
x(N+i)t ≤ yi ci i ∈ {1, . . . , M} (4f) TABLE 1
Average computation times for the MILP-based and
yi ∈ {0, 1} i ∈ {1, . . . , M} (4g) search-based algorithms, for various numbers of regular
xi(N+ j) ≤ y j ∀ (i, N + j) ∈ A : i ∈ {1, . . . , N} (4h) (N) and mobile backbone nodes (K) in the maximum fair
placement and assignment (MFPA) problem. All models
The objective of the Network Design MILP is to maximize
were formulated in GAMS 22.9 and solved using ILOG
the flow x through the graph (Eq. (4a)). The constraints state
CPLEX 11.2.0 on a 3.16 GHz Intel Xeon CPU with 3.25
that K arcs (mobile backbone node locations) must be selected
GB of RAM.
(4b), flow through all internal nodes must be conserved (4c),
arc capacities must be observed (4d - 4f), and yi is binary for N K MILP Algorithm Search-based Algorithm
all i (4g). Constraint 4h is a valid inequality that decreases 3 2 .92 sec 3.12 sec
computation time by reducing the size of the feasible set 4 2 1.24 sec 14.97 sec
in the LP relaxation [22]. Note that, for a given specification 5 2 1.35 sec 45.15 sec
of the y vector, all flows x are integer in all basic feasible 6 2 1.37 sec 1 min 28 sec
solutions of the resulting (linear) maximum flow problem. 6 3 1.45 sec 5 min 44 sec
This network design problem exactly corresponds to the 8 3 1.95 sec 33 min
mobile backbone network optimization problem as posed in 10 3 2.23 sec 2 hr 6 min
this section. The geometry of the mobile backbone network 15 5 5.06 sec 5 hr 4 min
problem is described by the arcs connecting node sets N
and M, while both the throughput function and the desired O(log(N)) times for different throughput values in order to
minimum throughput level are captured in the capacities of find the maximum throughput value such that all regular
the arcs connecting nodes in M to the sink, t. Any feasible nodes can be assigned. There are at most O(N 4 ) possible
placement of mobile backbone nodes and assignment of regu- values for the minimum throughput achieved by any
lar nodes is associated with a feasible solution to the network regular node; searching among these throughput values
design problem with the same objective value; likewise, any via binary search would require O(log(N)) solutions of
integer feasible solution to the network design problem yields the MILP problem.
a feasible placement and assignment in the mobile backbone Remark 2: It should be noted that the worst-case complexity of
network optimization problem, such that the number of regular mixed-integer linear programming is exponential in the num-
nodes assigned is equal to the volume of flow through the ber of binary variables. However, this approach performs well
network design graph. The equivalence of these two problems in practice, and simulation results indicate that it compares
is formally stated in Theorem 1: very favorably with the search-based approach developed in
Ref. [3] for the MFPA problem (See Table 1). Note that while
Theorem 1 Given an instance of the mobile backbone net- the computation time of the search-based algorithm increases
work design problem, the corresponding Network Design very rapidly with the problem size, the MILP-based algorithm
MILP yields an optimal solution to the mobile backbone node remains computationally tractable for problems of practical
placement and regular node assignment problems. scale.
Proof: The proof of Theorem 1 can be found in Ap-
pendix A. 3.2 Approximation algorithm
A solution to problem (4) provides both a placement of Table 1 indicates that the MILP formulation described by Eq. 4
mobile backbone nodes and an assignment of regular nodes provides an optimal solution in tractable time for moderately-
to mobile backbone nodes. Mobile backbone nodes are placed sized problems. However, this method is demonstrated to scale
at locations for which yi = 1, and regular node i is assigned poorly with problem size. Moreover, we have shown that the
to the mobile backbone node at location j if xi(N+ j) = 1. The network design problem on a network of the general form
number of regular nodes assigned is equal to the volume of shown in Figure 2 is NP-hard [23]. Therefore, an approxima-
flow through the graph. tion algorithm with computation time that is polynomial in the
We make the following observations about this algorithm: number of regular nodes and the number of mobile backbone
Remark 1: If K mobile backbone nodes are available and the nodes is desirable. This section describes such an algorithm.
goal is to assign as many regular nodes as possible such that The primary insight on which the approximation algorithm
a desired minimum throughput is achieved for each assigned is based is the fact that the maximum number of regular
regular node, the MILP problem in Eq. 4 needs only to be nodes that can be assigned is a submodular function of the
solved once for the desired throughput value and with a fixed set of mobile backbone node locations selected. Given a finite
value of K. However, we also note that the Network Design ground set D = {1, . . . , d}, a set function f (S) defined for all
MILP can be used as a subroutine in solving the maximum subsets S of D is said to be submodular if it has the property
fair placement and assignment (MFPA) problem considered that
in Ref. [3], in which the objective is to maximize the f (S ∪ {i, j}) − f (S ∪ {i}) ≤ f (S ∪ { j}) − f (S)
minimum throughput achieved by any regular node, such
that all regular nodes are assigned. To solve the MFPA for all i, j ∈ D, i = j and S ⊂ D {i, j} [24]. In the context
problem, it is necessary to solve the Network Design MILP of the network design problem, this means that the maximum
6. 6
flow through the network is a submodular function of the set Algorithm 1
of arcs incident to the sink that are selected. S←0 /
It has been shown [25] that for maximization of a nonde- max f low ← 0
creasing submodular set function f , where f (0) = 0, greedy
/ for k=1 to K do
selection of elements yields a performance guarantee of for m=1 to M do
1 − (1 − P )P > 1 − 1 , where P is the number of elements
1
e
if f (S ∪ {m}) ≥ max f low then
to be selected from the ground set and e is the base of the max f low ← f (S ∪ {m})
natural logarithm. This means that if an exact algorithm selects m∗ ← m
P elements from the ground set and produces a solution of end if
value OPT , a greedy selection of P elements (i.e., selection end for
via a process in which element i is selected if it is the S ← S ∪ {m∗ }
element that maximizes f (S ∪ {i}), where S is the set of end for
elements already selected) produces a solution of value at least return S
1
(1 − (1 − P )P ) · OPT .
For the network design problem considered in this paper,
P = K (the number of mobile backbone nodes that are to be until |S| = K. Algorithm 1 then returns set S. The performance
placed), and OPT is the number of regular nodes that are of Algorithm 1 is described by Theorem 2.
assigned in an optimal solution. Note that greedy selection of
K arcs amounts to solving at most O(N 3 K) linear maximum Theorem 2 Algorithm 1 returns a solution S such that f (S) ≥
flow problems on graphs with at most N + K + 2 nodes. Thus, (1 − 1 ) · f (S∗ ) , where S∗ is the optimal solution to the
e
the computation time of the greedy algorithm is polynomial network design problem on G.
in the number of regular nodes and the number of mobile
Proof: This follows from the fact that all maximum flows
backbone nodes. Furthermore, each of the maximum flow
through G are integer, and from the observation that the
problems solved by the greedy algorithm is solved over a
maximum flow that can be routed through G is a submodular
bipartite graph with node sets N∪{t} and {s}∪K, where K
function of S, the set of arcs that are selected.
is the set of nodes from M whose outgoing arcs are selected.
Because maximum flow problems can be solved even more
efficiently in bipartite networks than in general networks 3.3 Experimental evaluation of approximation algo-
[21], the greedy algorithm is thus highly efficient. Further rithm
computational efficiency can result from exploitation of max As described in Section 3.2, greedy selection of mo-
flow/min cut duality [23]. bile backbone node locations results in assignment of at
The submodularity of the network design objective is for- 1
least (1 − (1 − K )K ) · OPT ≥ (1 − 1 ) · OPT regular nodes,
e
mally stated in Lemma 1: where K is the number of mobile backbone nodes that are to
be placed and OPT is the number of regular nodes assigned
Lemma 1 If G is a graph in the network design problem by an exact algorithm (such as the MILP algorithm described
described in Section 3.1, the maximum flow that can be routed in Section 3.1) [25]. While such worst-case performance
through G is a submodular function of the set of arcs selected. guarantees are quite useful, it is also worthwhile to examine
the typical performance of the approximation algorithm on
Proof: The proof of Lemma 1 can be found in Ap- many problems.
pendix B. To this end, we have performed computational experiments
Lemma 1 implies that greedy selection of mobile backbone on a number of problems of various degrees of complexity.
node locations (i.e., selection via a process that maximizes the Regular node locations were generated randomly in a finite
total number of regular nodes assigned for each incremental 2-dimensional area, and a moderate throughput value was
selection of a new mobile backbone node location) yields prov- specified (i.e., one high enough such that there was no trivial
ably good solution to the overall placement and assignment selection of mobile backbone node locations that would result
problem. in assignment of all regular nodes). Results were averaged
Given a network design graph G, K mobile backbone nodes over a number of trials for each problem dimension.
and M possible mobile backbone node locations, and denoting Fig. 3 shows the performance of the approximation algo-
by f the maximum flow through G as a function of the set of rithm relative to the exact (MILP) algorithm. In Fig. 3(a),
mobile backbone node locations selected, this greedy selection the average percentage of regular nodes assigned by the
process is described by Algorithm 1. Algorithm 1 begins with exact algorithm that are also assigned by the approximation
an empty set of selected mobile backbone node locations, S, algorithm is plotted, along with the theoretical lower bound
and incrementally adds K elements to this set. In each of of (1 − 1 ) · OPT , for various problem sizes. In this fig-
e
K rounds of selection, M − |S| maximum flow problems are ure, a data point at 100% would mean that, on average,
solved on graphs consisting of nodes s, t, N, S and each of the approximation algorithm assigned as many regular nodes
the M − |S| nodes belonging to set MS. In each round of as the exact algorithm for that particular problem size. As
selection, the node from set MS that maximizes the total the graph shows, the approximation algorithm consistently
flow through G is added to set S, and this process continues exceeds the theoretical performance guarantee and achieves
7. 7
nearly the same level of performance as the exact algorithm
for all problem sizes considered.
Fig. 3(b) shows the computation time required for each of
these algorithms, plotted on a logarithmic axis. As the figure
shows, the computation time required for the approximation
algorithm scales gracefully with problem size. The average
computation time of the approximation algorithm was about 15
seconds for N = 100 and K = 14, whereas the MILP algorithm
took nearly twelve minutes to solve a problem of this size. The
significant improvement in computation time achieved by the
approximation algorithm makes it appropriate for some real-
time applications, while the exact algorithm is a promising
candidate for one-time design problems involving significant
costs.
Both the MILP algorithm and the approximation algorithm
(a) Performance of the approximation algorithm developed in this paper,
were formulated in GAMS 22.9 and solved using ILOG relative to an exact solution technique, in terms of number of regular nodes
CPLEX 11.2.0 on a 3.16 GHz Intel Xeon CPU with 3.25 GB assigned at the given throughput level.
of RAM.
4 J OINT PLACEMENT OF REGULAR AND MO -
BILE BACKBONE NODES
As described in Section 3, existing problem formulations in
the study of mobile backbone networks have assumed that the
locations of regular nodes are fixed a priori and that only
the locations of mobile backbone nodes are variable [18], [3],
[6]. This assumption is reasonable for some applications, such
as scenarios that involve mobile agents extracting data from a
fixed sensor network. However, in many applications the loca-
tions of both regular nodes and mobile backbone nodes can be
controlled. For example, a heterogeneous system composed of
air and ground vehicles conducting ground measurements in an
urban environment can be appropriately modeled as a mobile
(b) Computation time of the approximation algorithm and the exact (MILP)
backbone network: the ground vehicles are well positioned to algorithm for various problem sizes. Due to the large range of values
make observations of phenomena at ground level, but their represented, a logarithmic scale is used.
movement and communication are hindered by surrounding
obstacles. Air vehicles, on the other hand, are poorly equipped Fig. 3. Comparison of the exact and approximation
to observe events on the ground but can easily move above algorithms developed in this section. Although the MILP-
ground obstacles and communicate. based exact algorithm developed in this section signif-
This section develops a modeling framework and solution icantly outperforms existing techniques in terms of re-
technique that are appropriate for problems of this nature. We quired computation time, our experiments indicate that
assume that L candidate regular node locations are available a the greedy approximation algorithm achieves nearly the
priori, perhaps selected by heuristic means or due to logistical same level of performance with an even greater reduction
constraints. Each of N regular nodes (N ≤ L) must occupy one in computation time.
of these locations, and no two regular nodes can be assigned
to the same location. Given an initial location and a mobility
constraint, each regular node is capable of reaching a subset reachable from each of the initial regular node locations); and
of the other locations. There are K mobile backbone nodes the decision variables as Fi (the final locations of the regular
(K ≤ N) that can be placed anywhere, a throughput function τ nodes), Mi (the selected locations of the mobile backbone
is specified, and a desired minimum throughput τmin is given. nodes, i = 1, . . . , K), and A (the assignment of regular nodes
Given these assumptions, the goal of this section is to place to mobile backbone nodes), this optimization problem is:
both the regular nodes and mobile backbone nodes while max Fτ (F, M, A, τmin )
simultaneously assigning regular nodes to mobile backbone F, M, A
nodes in order to maximize the number of regular nodes that subject to Fi ∈ r(Ii ), i = 1, . . . , N
are successfully assigned and achieve the desired minimum Mi ∈ C(I), i = 1, . . . , K
throughput level τmin , under the given throughput function τ.
A∈A
Denoting the problem data as Ii (the initial locations of
the regular nodes, i = 1, . . . , N) and and r(Ii ) (the locations where Fτ (F, M, A, τmin ) is the number of regular nodes that
8. 8
N+1 N+L+1 N+2L+1
placement and assignment of regular and mobile backbone
1 nodes is associated with a feasible solution to the network
N+2 N+L+2
N+2L+2 design problem; likewise, any feasible solution to the network
y1 c1 design problem yields a feasible placement and assignment in
2
N+2L+3 the mobile backbone network optimization problem.
y2 c2
Denote the set of nodes in the network design graph by
…
…
y3 c3 N and the set of arcs by A . If K mobile backbone nodes
…
…
N+i N+L+i t are available and a minimum throughput level is specified, the
s
i yjcj goal of the network design problem is to select K arcs from
N+2L+j {N + 2L + 1, . . . , N + 2L + M} and a feasible flow xi j , (i, j) ∈
A such that the s −t flow is maximized. This problem can be
…
yM cM solved via the following MILP:
…
…
… N
max ∑ xsi (5a)
N x,y
i=1
M
N+L N+2L N+2L+O(N3) subject to ∑ yi = K (5b)
i=1
Fig. 4. The network design problem corresponding to ∑ xi j = ∑ xli i ∈ N {s,t} (5c)
the joint placement and assignment problem for mobile j:(i, j)∈A l:(l,i)∈A
backbone networks, with regular node mobility. Unlabeled xi j ≥ 0 ∀ (i, j) ∈ A (5d)
arc capacities are equal to one. For clarity, not all arcs and
xi j ≤ 1 ∀ (i, j) ∈ A : j ∈ N {t} (5e)
nodes are shown.
x(N+2L+i)t ≤ yi ci i ∈ {1, . . . , M} (5f)
yi ∈ {0, 1} i ∈ {1, . . . , M} (5g)
achieve throughput level τmin , given node placements F and
M, assignment A, and throughput function τ. A denotes the x(N+L+i)(N+2L+ j) ≤ y j (N + L + i, N + 2L + j) ∈ A : i ∈ {1, ..., L}
set of valid assignments, while C denotes the 1-centers of (5h)
candidate regular node locations. where the constraints state that K arcs (mobile backbone node
locations) must be selected (5b), flow through all internal
4.1 Network design formulation nodes must be conserved (5c), arc capacities must be observed
(5d- 5f), and yi is binary for all i (5g). Constraint 5h is again
Optimal simultaneous placement and assignment of regular
a valid inequality included to reduce computation time by
nodes and mobile backbone nodes is again achieved through
strengthening the LP relaxation [22].
the solution of a network design problem.
The network design graph over which this optimization Fig. 5 shows an example of a solution to the simultaneous
takes place is schematically represented in Fig. 4. This graph is placement and assignment problem with regular node move-
similar to that shown in Fig. 2, with the exception that sets of ment. The regular nodes, initially in positions indicated by •,
nodes L= {N + 1, . . . , N + L} and L = {N + L + 1, . . . , N + 2L} are able to move to other locations (◦) within their radii of
are added. These nodes represent locations to which regular motion, indicated by shaded circles. This initial configuration
nodes may move. Node i ∈N is connected to node N + j ∈L if, is shown in Fig. 5(a). In an optimal solution to this problem,
and only if, regular node i can reach sensing location j under shown in Fig. 5(b), the regular nodes have moved such that
its mobility constraint. Each node N + i ∈L is connected to they are grouped into compact clusters for which the mobile
node N + L + i ∈L via an arc of unit capacity. This enforces backbone nodes can provide an effective communication in-
the constraint that at most one regular node can occupy each frastructure. The clusters are relatively balanced, in that the
location. Finally, node N + L + i ∈L is connected to node clusters with larger radii tend to have fewer regular nodes,
N + 2L + j ∈M if, and only if, sensing location i is within while the more compact clusters can accommodate more regu-
the 1-center radius of 1-center j. Finally, each node in M is lar nodes and still achieve the desired minimum throughput. In
connected to the sink t, and the capacity of the arc connecting this example, all regular nodes have been successfully assigned
N + 2L + i ∈M to t is again the product of yi and ci . to mobile backbone nodes.
This network design problem exactly describes the mobile This algorithm is designed maximize the number of regular
backbone network optimization problem with mobile regular nodes that are assigned at throughput level τmin . If, instead,
nodes. The arcs connecting node sets N and L reflect the the goal is to achieve the best possible minimum throughput
mobility constraints of the regular nodes, while the geometric such that all regular nodes are assigned to a mobile backbone
aspects of the mobile backbone node placement problem are node (i.e., to solve the MFPA problem), it is necessary to
described by the arcs connecting node sets L and M. As solve the MILP problem in Eq. 5 O(log(L)) times for different
in Section 3, both the throughput function and the desired throughput values (which result in different values for the ci ’s
minimum throughput level are captured in the capacities of in the network design problem).
the arcs connecting nodes in M to the sink, t. Any feasible In this paper, all candidate regular node locations are
9. 9
(a) Initial regular node placement, with radius of motion for (b) An optimal placement of regular and mobile backbone
each regular node. nodes.
Fig. 5. A small example of mobile backbone network optimization with limited regular node movement. Open circles
represent possible regular node locations, and filled circles are the initial locations of the regular nodes. Shaded circles
in the left figure indicate the possible radius of motion of each regular node. In the right figure, mobile backbone nodes
are placed such that they provide communication support for the regular nodes. Each regular node is assigned to at
most one mobile backbone node. Dotted lines indicate regular node motion in this optimal solution. Dashed circles
indicate the communication radius of each cluster of nodes. In this example, all regular nodes have been successfully
assigned to mobile backbone nodes.
considered to be equally valuable – that is, a regular node Algorithm 2
that transmits to a mobile backbone node from location i S←0 /
contributes as much to the objective as a mobile backbone max f low ← 0
node transmitting from location j. However, this formulation for k=1 to K do
can easily be modified to model variably valuable sensing for m=1 to M do
locations by replacing the objective function with if f (S ∪ {m}) ≥ max f low then
max f low ← f (S ∪ {m})
L
m∗ ← m
max ∑ vi xN+i,N+L+i
x,y
i=1
end if
end for
where vi is the value of location i. S ← S ∪ {m∗ }
end for
4.2 Approximation Algorithm return S
While the MILP-based algorithm described in Section 4.1
provides an exact solution to the mobile backbone network
Lemma 2 motivates consideration of a greedy algorithm
optimization problem, its worst-case computation time is again
for the problem of maximizing the number of regular nodes
exponential in the number of binary variables. Fortunately, the
that achieve throughput level τmin . Given a network design
submodularity property described in Section 3.2 also holds for
graph G of the form shown in Figure 4, K mobile backbone
graphs of the form shown in Figure 4:
nodes and M possible mobile backbone node locations, and
denoting by f the maximum flow through G as a function of
Lemma 2 If G is a graph in the network design problem the set of mobile backbone node locations selected, this greedy
described in Section 4.1, the maximum flow that can be routed algorithm is described by Algorithm 2. Theorem 3 describes
through G is a submodular function of the set of arcs selected. the performance of Algorithm 2:
Proof: The proof of Lemma 2 is similar to that of
Lemma 1, with the exception that the reduction to a bipartite Theorem 3 Algorithm 2 returns a solution S such that f (S) ≥
matching problem is replaced with a reduction to a node- (1 − 1 ) · f (S∗ ) , where S∗ is the optimal solution to the
e
disjoint path problem on a tripartite graph. network design problem on G.
10. 10
1
Proof: This follows from the fact that all maximum flows
fraction of regular nodes assigned
through G are integer, and from the observation that the 0.95 approximation algorithm
maximum flow that can be routed through G is a submodular theoretical lower bound
function of S, the set of arcs that are selected. 0.9
Thus, Algorithm 2 is an approximation algorithm with 0.85
approximation guarantee 1 − 1 . Additionally, because each
e
round of greedy selection consists of solving a polynomial 0.8
number of maximum flow problems on graphs with at most
0.75
N + 2L + K + 2 nodes, and there are K rounds of selection,
the running time of Algorithm 2 is polynomial in the number 0.7
of regular nodes, the number of locations, and the number
of mobile backbone nodes. Furthermore, all network flow 0.65
problems solved by Algorithm 2 are formulated on bipartite
graphs, for which highly efficient algorithms exist [21]. N=40, K=8 N=50, K=9 N=60, K=10 N=70, K=11 N=80, K=12 N=90, K=13
problem size
The performance of Algorithm 2 relative to the exact
(MILP) algorithm developed in this section is shown in Fig- (a) Performance of the approximation algorithm developed in this section,
relative to an exact solution technique, in terms of number of regular nodes
ure 6. Again, the approximation algorithm exhibits excellent assigned at the given throughput level.
empirical performance, achieving results comparable to those
4
of the exact algorithm with a great reduction in computation 10
time. The results shown in Figure 6 were obtained from models approximation algorithm
formulated in GAMS 22.9 and solved using ILOG CPLEX
computation time (seconds)
exact algorithm
11.2.0 on a 3.16 GHz Intel Xeon CPU with 3.25 GB of RAM. 10
3
5 C ONCLUSIONS 10
2
This work has described new algorithms for solving the
problem of mobile backbone network optimization. Exact 1
10
MILP-based techniques and the first known approximation
algorithms with computation time polynomial in the number
of regular nodes and the number of mobile backbone nodes
0
were described. 10
N=40, K=8 N=50, K=9 N=60, K=10 N=70, K=11 N=80, K=12 N=90, K=13
Based on simulation results, we conclude that the MILP- problem size
based approach provides a considerable computational advan- (b) Computation time of the approximation algorithm and the exact (MILP)
tage over existing techniques for mobile backbone network algorithm for various problem sizes. Due to the large range of values
represented, a logarithmic scale is used.
optimization. This approach has been successfully applied to
a problem in which a maximum number of regular nodes are Fig. 6. Comparison of the exact and approximation algo-
to be assigned to mobile backbone nodes at a given level rithms developed in this section. On average, the approx-
of throughput, and to a related problem from the literature imation algorithm greatly exceeded its performance guar-
in which all regular nodes are to be assigned to a mobile antee, achieving nearly the same level of performance as
backbone node such that the minimum throughput achieved the exact algorithm for all problem sizes considered. In all
by any regular node is maximized. cases, L = 1.5N.
For cases in which a MILP approach is impractical due
to constraints on computation time, the greedy approximation
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Ideas, 2005, p. 88. is also now satisfied for all arcs. Furthermore, constraint 4c is
[25] G. Nemhauser and L. Wolsey, “Maximizing submodular set functions: satisfied for nodes N + 1, ..., N + M; node N + k has |Ak | units
Formulations and Analysis of Algorithms,” Studies on Graphs and of flow incoming and outgoing for k = 1, ..., K, and zero units
Discrete Programming, P. Hansen, ed., 1981, pp. 279-301.
[26] A. S. Asratian, T. M. J. Denley and R. H¨ ggkvist, Bipartite Graphs and
a of flow incoming and outgoing for k = K + 1, ..., M. Thus, all
their Applications. Cambridge University Press, 1998. constraints are satisfied, and the objective value of this solution
is equal to the number of regular nodes that were assigned in
the original solution, i.e., ∑K |Ak |.
A PPENDIX A k=1
Now, assume that we are given a feasible solution to the
P ROOF OF T HEOREM 1 network design problem and its associated MILP. Furthermore,
Proof: Given a feasible solution to the original problem assume that all flows in this solution are integer. (By virtue
(i.e., a solution in which K mobile backbone nodes are placed of the total unimodularity of the constraint matrix in the
anywhere in the plane, each regular node is assigned to at maximum flow problem and the integrality of the right hand
most one mobile backbone node, and every assigned regular side vector, all basic feasible solutions of the linear program
node achieves throughput at least τmin ), a feasible solution to induced by any feasible choice of the y vector are integer.)
the corresponding network design problem and its associated Since all flows are integer, flows along arcs terminating in
Network Design MILP (4) can be constructed as follows: node sets N and M are either 0 or 1. Again, assume without
12. 12
1
loss of generality that the nodes are labeled such that y1 , ..., yK N+1
are equal to 1, and yK+1 , ..., yM are equal to 0. Thus, no flow
c1=1
traverses nodes N + K + 1, ..., N + M. 2
To construct a feasible solution to the mobile backbone
s N+2 c2=3
network optimization problem, first place mobile backbone t
3
nodes at the K locations l1 , ..., lK corresponding to nodes
c3=2
N + 1, ..., N + K in the network design graph. Next, for each
mobile backbone node k = 1, ..., K, let Ak be the set of regular N+3
nodes for which xi(N+k) = 1. Assign the regular nodes in set N=4
Ak to regular node k. Note that each regular node is assigned (a) A graph over which a maximum flow problem can be
to at most one mobile backbone node, since at most one unit formulated. Unlabeled arc capacities are equal to one.
of flow can traverse each node 1, ..., N. Furthermore, note that
1
each assigned regular node achieves throughput at least τmin by N+1
definition of the arc capacity ck . The number of regular nodes 2
assigned in this solution is equal to ∑K |Ak |. For each mobile
k=1
backbone node k, |Ak | is equal to the flow traversing nodes
N+2
N + k. Since no flow traverses nodes N + K + 1, ..., N + M, the 3
total flow through the graph is equal to ∑K |Ak |. Thus, the
k=1
two solutions have the same objective value.
We have shown that for every feasible solution to the orig- N=4
N+3
inal problem, there is a feasible solution to the corresponding
(b) A bipartite matching problem that is equivalent to the
network design problem and its associated MILP with the maximum flow problem above.
same objective value. Thus, although the restriction of mobile
backbone nodes to the 1-center locations of regular nodes Fig. 7. An example of conversion from a maximum flow
may exclude an uncountable number of optimal solutions to problem to an equivalent bipartite matching problem, for
the original placement and assignment problem, it does not N = 4, M = 3.
exclude all optimal solutions. Furthermore, we have shown
that for every integer solution to the network design problem
and its associated MILP (including the optimal solution), there original node N + i. Thus, each node N + i in the maximum
is a feasible solution to the original problem with the same flow problem becomes a set of nodes N + i in the bipartite
objective value. Thus, the MILP formulation cannot produce matching problem, and the cardinality of this set is equal to
a solution with a higher objective value than is possible in ci . An example of this reformulation is shown in Fig. 7.
the original problem. Therefore, the MILP formulation can be For any feasible flow in the original graph, there is a corre-
used to obtain a solution to the original problem that achieves sponding matching in the bipartite graph with cardinality equal
the same optimal objective value that was possible in the to the volume of flow; likewise, for any feasible matching in
original problem. the bipartite graph, there is a corresponding flow of volume
equal to the cardinality of the matching. Therefore, the volume
of the maximum flow through the original graph is equal to
A PPENDIX B the cardinality of a maximum matching in the bipartite graph.
P ROOF OF L EMMA 1 The graphs expressing the relation in Eq. (6) are shown in
Proof: We begin by restating the submodularity condition the top row of Fig. 8: the sum of the maximum flows through
as follows: the left two graphs must be less than or equal to the sum of
the maximum flows through the right two graphs.
f ∗ (S ∪ {i, j}) + f ∗ (S) ≤ f ∗ (S ∪ {i}) + f ∗ (S ∪ { j}) (6) Converting these maximum flow problems into their equiv-
alent bipartite matching problems, we obtain the condition
where f ∗ is the maximum flow through G, as a function of the
that the sum of the cardinalities of maximum matchings in
set of selected arcs. Next, we note that for a fixed selection
bipartite graphs G1 and G2 in Fig. 8 is at most the sum of the
of arcs S, the problem of finding the maximum flow through
cardinalities of maximum matchings in G3 and G4 .
G can be expressed as an equivalent maximum matching
Consider a maximum matching M1 in graph G1 , and denote
problem on a bipartite graph with node sets L and R2 . This is
its cardinality by Ns . This means that Ns nodes from set S are
accomplished as follows: node set L in the bipartite matching
covered by matching M1 . Note that M1 is a feasible matching
problem is simply node set N in the maximum flow problem.
for G2 as well, since all arcs in G1 are also present in G2 .
Node set R is derived from node set M in the maximum flow
It is a property of bipartite graphs that if a matching Q is
problem, with one modification: if the arc from node N +i ∈ M
feasible for a graph H, then there exists a maximum matching
to t has outgoing capacity ci , then R contains ci copies of node
Q∗ in H such that all of the nodes covered by Q are also
N +i, each of which is connected to the same nodes in L as the
covered by Q∗ [26]. Denote such a maximum matching for
2. A set of edges in a graph is a matching if no two edges share a common matching M1 in graph G2 by M2 , and note that Ns nodes from
end node. A maximum matching is a matching of maximum cardinality [26]. set S are covered by M2 . Denote the number of nodes covered
13. 13
1 1 1 1
c1 c1 c1 c1
2 S 2 S 2 S 2 S
…
…
…
…
… …
… …
… …
… …
…
…
…
…
cT
ci
…
…
…
…
ci
cj cj
i i
N N j N N j
1 1 1 1
2 2 2 2
S S S S
…
…
…
…
…
…
…
… …
… …
… …
… …
…
…
…
…
i |i|=ci i |i|=ci
N N j |j|=cj N N j |j|=cj
|S|=∑k=1,…,T ck
G1 G2 G3 G4
Fig. 8. Schematic representation of the graphs involved in the proof of the submodularity condition. The top graphs
relate to the original maximum flow problem, while the bottom graphs are their equivalent reformulations in the bipartite
matching problem. For clarity, not all arcs are shown.
by M2 in node sets i and j by Ni and N j , respectively. Then,
the total cardinality of these maximum matchings for graphs
G1 and G2 is equal to 2Ns + Ni + N j .
Now consider the matching obtained by removing the edges
incident to node set j from M2 . Note that this matching is
feasible for graph G3 , and its cardinality is Ns + Ni . Likewise,
the matching obtained by removing the edges incident to node
set i from M2 is feasible for graph G4 , and its cardinality is
Ns +N j . Since these matchings are feasible (but not necessarily
optimal) for G3 and G4 , the sum of the cardinalities of maxi-
mum matchings for these graphs must be at least 2Ns +Ni +N j .
This establishes the submodularity property for the matching
problem as well as for the maximum flow problem.