The Graph is a powerful mathematical tool applied in many fields as transportation, communication,
informatics, economy, … In an ordinary graph, the weights of edges and vertexes are considered
independently where the length of a path is the sum of weights of the edges and the vertexes on this path.
However, in many practical problems, weights at a vertex are not the same for all paths passing this vertex
but depend on coming and leaving edges. The presented paper develops a model of the extended linear
multi-commodity multi-cost network that can be more exactly and effectively applied to model many
practical problems. Then, maximal limit cost flow problems are modeled as implicit linear programming
problems. On the base of dual theory in linear programming, an effective approximate algorithm is
developed.
One of the important steps in routing is to find a feasible path based on the state information. In order to support real-time multimedia applications, the feasible path that satisfies one or more constraints has to be computed within a very short time. Therefore, the paper presents a genetic algorithm to solve the paths tree problem subject to cost constraints. The objective of the algorithm is to find the set of edges connecting all nodes such that the sum of the edge costs from the source (root) to each node is minimized. I.e. the path from the root to each node must be a minimum cost path connecting them. The algorithm has been applied on two sample networks, the first network with eight nodes, and the last one with eleven nodes to illustrate its efficiency.
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
In machine learning, support vector machines (SVMs, also support vector networks[1]) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. The basic SVM takes a set of input data and predicts, for each given input, which of two possible classes forms the output, making it a non-probabilistic binary linear classifier.
Application of Fuzzy Algebra in Coding TheoryIJERA Editor
Fuzziness means different things depending upon the domain of application and the way it is measured. By
means of fuzzy sets, vague notions can be described mathematically now a vigorous area of research with
manifold applications. It should be mentioned that there are natural ways (not necessarily trivial) to fuzzily
various mathematical structures such as topological spaces, algebraic structure etc. The notion of L-fuzzy sets
later more generalizations were also made using various membership sets and operations. In this section we let F
denote the field of integers module 2, we define a fuzzy code as a fuzzy subset of Fn where Fn = {(a1, ....an | a i
F, i = 1, ...n} and n is a fixed arbitrary positive integers we recall that Fn is a vector space over F. We give an
analysis of the Hamming distance between two fuzzy code words and the error – correcting capability of a code
in terms of its corresponding fuzzy codes. The results appearing in the first part of this section are from [17].
Recent Advances in Natural Language ProcessingApache MXNet
This talk goes over the recent progress made in the Natural Language Processing field in terms of Language Representation. Starting with the classic tf-idf, we cover word2vec, ELMo, BERT, GPT-2 and XL-Net.
This deck was used for a ACNA2019 talk.
Slides: Thomas Delteil
One of the important steps in routing is to find a feasible path based on the state information. In order to support real-time multimedia applications, the feasible path that satisfies one or more constraints has to be computed within a very short time. Therefore, the paper presents a genetic algorithm to solve the paths tree problem subject to cost constraints. The objective of the algorithm is to find the set of edges connecting all nodes such that the sum of the edge costs from the source (root) to each node is minimized. I.e. the path from the root to each node must be a minimum cost path connecting them. The algorithm has been applied on two sample networks, the first network with eight nodes, and the last one with eleven nodes to illustrate its efficiency.
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
In machine learning, support vector machines (SVMs, also support vector networks[1]) are supervised learning models with associated learning algorithms that analyze data and recognize patterns, used for classification and regression analysis. The basic SVM takes a set of input data and predicts, for each given input, which of two possible classes forms the output, making it a non-probabilistic binary linear classifier.
Application of Fuzzy Algebra in Coding TheoryIJERA Editor
Fuzziness means different things depending upon the domain of application and the way it is measured. By
means of fuzzy sets, vague notions can be described mathematically now a vigorous area of research with
manifold applications. It should be mentioned that there are natural ways (not necessarily trivial) to fuzzily
various mathematical structures such as topological spaces, algebraic structure etc. The notion of L-fuzzy sets
later more generalizations were also made using various membership sets and operations. In this section we let F
denote the field of integers module 2, we define a fuzzy code as a fuzzy subset of Fn where Fn = {(a1, ....an | a i
F, i = 1, ...n} and n is a fixed arbitrary positive integers we recall that Fn is a vector space over F. We give an
analysis of the Hamming distance between two fuzzy code words and the error – correcting capability of a code
in terms of its corresponding fuzzy codes. The results appearing in the first part of this section are from [17].
Recent Advances in Natural Language ProcessingApache MXNet
This talk goes over the recent progress made in the Natural Language Processing field in terms of Language Representation. Starting with the classic tf-idf, we cover word2vec, ELMo, BERT, GPT-2 and XL-Net.
This deck was used for a ACNA2019 talk.
Slides: Thomas Delteil
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
Sequential and parallel algorithm to find maximum flow on extended mixed netw...csandit
The problem of finding maximum flow in network
graph is extremely interesting and
practically applicable in many fields in our daily
life, especially in transportation. Therefore, a
lot of researchers have been studying this problem
in various methods. Especially in 2013, we
has developed a new algorithm namely, postflow-pull
algorithm to find the maximum flow on
traditional networks. In this paper, we revi
sed postflow-push methods to solve this
problem of finding maximum flow on extended mixed
network. In addition, to take more
advantage of multi-core architecture of t
he parallel computing system, we build this
parallel algorithm. This is a completely new method
not being announced in the world. The
results of this paper are basically systematized an
d proven. The idea of this algorithm is using
multi processors to work in parallel by postflow_p
ush algorithm. Among these processors,
there is one main processor managing data, sending
data to the sub processors, receiving data
from the sub-processors. The sub-processors simulta
neously execute their work and send their
data to the main processor until the job is finishe
d, the main processor will show the results of
the problem.
On the performance of code word diversity based quasi orthogonal space time b...IJECEIAES
In the recent past, a lot of researches have been put into designing a MultipleInput-Multiple-Output (MIMO) system to provide multimedia services with higher quality and at higher data rate. On par with these requirements, a novel Quasi Orthogonal Space Time Block Code (QOSTBC) scheme based on code word diversity is proposed, which is a multi-dimensional approach, in this paper. The term code word diversity is coined, since the information symbols were spread across many code words in addition to traditional time and spatial spreading, without increasing transmission power and bandwidth. The receiver with perfect channel state information estimates the transmitted symbols with less probability of error, as more number of samples is available to estimate given number of symbols due to the extra diversity due to code words. The simulation results show a significant improvement in the Bit Error Rate (BER) performance of the proposed scheme when compared with the conventional schemes.
Bounds on the Achievable Rates of Faded Dirty Paper Channel IJCNCJournal
Bounds on the achievable rate of a Gaussian channel in the case that the transmitter knows the
interference signal but not its fading coefficients are given. We generalize the analysis which were studied
in [1] and [4] so that their results are special cases of our analysis. We enforce our bounds by simulations
in which many numerical examples are drawn and investigated under different cases.
EXTENDED LINEAR MULTICOMMODITY MULTICOST NETWORK ANDMAXIMAL CONCURENT FLOW PR...ijmnct
Graph is a powerful mathematical tool applied in many fields as transportation, communication,
informatics, economy, … In ordinary graph the weights of edges and vertexes are considered indepently
where the length of a path is the sum of weights of the edges and the vertexes on this path. However, in
many practical problems, weights at a vertex are not the same for all paths passing this vertex, but depend
on coming and leaving edges. In the article [2], a kind of weights, called switch cost, is defined. The papers
[3-6] study multicomodity flow problems in ordinary networks. The papers [3-6] study multicomodity flow
problems in extended networks, where switch costs are defined for mixed graphs. The papers [12,13]
develops a model of extended linear multicommodity multicost network and studies the maximal linear
multicomodity multicost flow problems. The papers [14,15] study the maximal multicomodity multicost
flow limited cost problems. Model of extended linear multicommodity multicost network can be applied to
modelize many practical problems more exactly and effectively. The presented paper studies the maximal
concurent linear multicomodity multicost flow problems, that are modelized as implicit linear
programming problems. On the base of dual theory in linear programming an effective aproximate
algorithms is developed.
EXTENDED LINEAR MULTICOMMODITY MULTICOST NETWORK ANDMAXIMAL CONCURENT FLOW PR...ijmnct
Graph is a powerful mathematical tool applied in many fields as transportation, communication,
informatics, economy, … In ordinary graph the weights of edges and vertexes are considered indepently
where the length of a path is the sum of weights of the edges and the vertexes on this path. However, in
many practical problems, weights at a vertex are not the same for all paths passing this vertex, but depend
on coming and leaving edges. In the article [2], a kind of weights, called switch cost, is defined. The papers
[3-6] study multicomodity flow problems in ordinary networks. The papers [3-6] study multicomodity flow
problems in extended networks, where switch costs are defined for mixed graphs. The papers [12,13]
develops a model of extended linear multicommodity multicost network and studies the maximal linear
multicomodity multicost flow problems. The papers [14,15] study the maximal multicomodity multicost
flow limited cost problems. Model of extended linear multicommodity multicost network can be applied to
modelize many practical problems more exactly and effectively. The presented paper studies the maximal
concurent linear multicomodity multicost flow problems, that are modelized as implicit linear
programming problems. On the base of dual theory in linear programming an effective aproximate
algorithms is developed.
Algorithm Finding Maximum Concurrent Multicommodity Linear Flow with Limited ...IJCNCJournal
Graphs and extended networks are is powerful mathematical tools applied in many fields as transportation,
communication, informatics, economy, … Algorithms to find Maximum Concurrent Multicommodity Flow
with Limited Cost on extended traffic networks are introduced in the works we did. However, with those
algorithms, capacities of two-sided lines are shared fully for two directions. This work studies the more
general and practical case, where flows are limited to use two-sided lines with a single parameter called
regulating coefficient. The algorithm is presented in the programming language Java. The algorithm is
coded in programming language Java with extended network database in database management system
MySQL and offers exact results.
SEQUENTIAL AND PARALLEL ALGORITHM TO FIND MAXIMUM FLOW ON EXTENDED MIXED NETW...cscpconf
The problem of finding maximum flow in network graph is extremely interesting and
practically applicable in many fields in our daily life, especially in transportation. Therefore, a
lot of researchers have been studying this problem in various methods. Especially in 2013, we
has developed a new algorithm namely, postflow-pull algorithm to find the maximum flow on
traditional networks. In this paper, we revised postflow-push methods to solve this
problem of finding maximum flow on extended mixed network. In addition, to take more
advantage of multi-core architecture of the parallel computing system, we build this
parallel algorithm. This is a completely new method not being announced in the world. The
results of this paper are basically systematized and proven. The idea of this algorithm is using
multi processors to work in parallel by postflow_push algorithm. Among these processors,
there is one main processor managing data, sending data to the sub processors, receiving data
from the sub-processors. The sub-processors simultaneously execute their work and send their
data to the main processor until the job is finished, the main processor will show the results of
the problem.
An Ant Algorithm for Solving QoS Multicast Routing ProblemCSCJournals
Abstract: Many applications require send information from a source to multiple destinations through a communication network. To support these applications, it is necessary to determine a multicast tree of minimal cost to connect the source node to the destination nodes subject to delay constraints. Based on the Ant System algorithm, we present an ant algorithm to find the multicast tree that minimizes the total cost. In the proposed algorithm, the k shortest paths from the source node to the destination nodes are used for genotype representation. The expermintal results show that the algorithm can find optimal solution quickly and has a good scalability.
In this paper, we solve this problem of finding maximum flow in extended mixed network by Revisedpreflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15]
In this paper, we solve this problem of finding maximum flow in extended mixed network by Revised preflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15].
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
Sequential and parallel algorithm to find maximum flow on extended mixed netw...csandit
The problem of finding maximum flow in network
graph is extremely interesting and
practically applicable in many fields in our daily
life, especially in transportation. Therefore, a
lot of researchers have been studying this problem
in various methods. Especially in 2013, we
has developed a new algorithm namely, postflow-pull
algorithm to find the maximum flow on
traditional networks. In this paper, we revi
sed postflow-push methods to solve this
problem of finding maximum flow on extended mixed
network. In addition, to take more
advantage of multi-core architecture of t
he parallel computing system, we build this
parallel algorithm. This is a completely new method
not being announced in the world. The
results of this paper are basically systematized an
d proven. The idea of this algorithm is using
multi processors to work in parallel by postflow_p
ush algorithm. Among these processors,
there is one main processor managing data, sending
data to the sub processors, receiving data
from the sub-processors. The sub-processors simulta
neously execute their work and send their
data to the main processor until the job is finishe
d, the main processor will show the results of
the problem.
On the performance of code word diversity based quasi orthogonal space time b...IJECEIAES
In the recent past, a lot of researches have been put into designing a MultipleInput-Multiple-Output (MIMO) system to provide multimedia services with higher quality and at higher data rate. On par with these requirements, a novel Quasi Orthogonal Space Time Block Code (QOSTBC) scheme based on code word diversity is proposed, which is a multi-dimensional approach, in this paper. The term code word diversity is coined, since the information symbols were spread across many code words in addition to traditional time and spatial spreading, without increasing transmission power and bandwidth. The receiver with perfect channel state information estimates the transmitted symbols with less probability of error, as more number of samples is available to estimate given number of symbols due to the extra diversity due to code words. The simulation results show a significant improvement in the Bit Error Rate (BER) performance of the proposed scheme when compared with the conventional schemes.
Bounds on the Achievable Rates of Faded Dirty Paper Channel IJCNCJournal
Bounds on the achievable rate of a Gaussian channel in the case that the transmitter knows the
interference signal but not its fading coefficients are given. We generalize the analysis which were studied
in [1] and [4] so that their results are special cases of our analysis. We enforce our bounds by simulations
in which many numerical examples are drawn and investigated under different cases.
EXTENDED LINEAR MULTICOMMODITY MULTICOST NETWORK ANDMAXIMAL CONCURENT FLOW PR...ijmnct
Graph is a powerful mathematical tool applied in many fields as transportation, communication,
informatics, economy, … In ordinary graph the weights of edges and vertexes are considered indepently
where the length of a path is the sum of weights of the edges and the vertexes on this path. However, in
many practical problems, weights at a vertex are not the same for all paths passing this vertex, but depend
on coming and leaving edges. In the article [2], a kind of weights, called switch cost, is defined. The papers
[3-6] study multicomodity flow problems in ordinary networks. The papers [3-6] study multicomodity flow
problems in extended networks, where switch costs are defined for mixed graphs. The papers [12,13]
develops a model of extended linear multicommodity multicost network and studies the maximal linear
multicomodity multicost flow problems. The papers [14,15] study the maximal multicomodity multicost
flow limited cost problems. Model of extended linear multicommodity multicost network can be applied to
modelize many practical problems more exactly and effectively. The presented paper studies the maximal
concurent linear multicomodity multicost flow problems, that are modelized as implicit linear
programming problems. On the base of dual theory in linear programming an effective aproximate
algorithms is developed.
EXTENDED LINEAR MULTICOMMODITY MULTICOST NETWORK ANDMAXIMAL CONCURENT FLOW PR...ijmnct
Graph is a powerful mathematical tool applied in many fields as transportation, communication,
informatics, economy, … In ordinary graph the weights of edges and vertexes are considered indepently
where the length of a path is the sum of weights of the edges and the vertexes on this path. However, in
many practical problems, weights at a vertex are not the same for all paths passing this vertex, but depend
on coming and leaving edges. In the article [2], a kind of weights, called switch cost, is defined. The papers
[3-6] study multicomodity flow problems in ordinary networks. The papers [3-6] study multicomodity flow
problems in extended networks, where switch costs are defined for mixed graphs. The papers [12,13]
develops a model of extended linear multicommodity multicost network and studies the maximal linear
multicomodity multicost flow problems. The papers [14,15] study the maximal multicomodity multicost
flow limited cost problems. Model of extended linear multicommodity multicost network can be applied to
modelize many practical problems more exactly and effectively. The presented paper studies the maximal
concurent linear multicomodity multicost flow problems, that are modelized as implicit linear
programming problems. On the base of dual theory in linear programming an effective aproximate
algorithms is developed.
Algorithm Finding Maximum Concurrent Multicommodity Linear Flow with Limited ...IJCNCJournal
Graphs and extended networks are is powerful mathematical tools applied in many fields as transportation,
communication, informatics, economy, … Algorithms to find Maximum Concurrent Multicommodity Flow
with Limited Cost on extended traffic networks are introduced in the works we did. However, with those
algorithms, capacities of two-sided lines are shared fully for two directions. This work studies the more
general and practical case, where flows are limited to use two-sided lines with a single parameter called
regulating coefficient. The algorithm is presented in the programming language Java. The algorithm is
coded in programming language Java with extended network database in database management system
MySQL and offers exact results.
SEQUENTIAL AND PARALLEL ALGORITHM TO FIND MAXIMUM FLOW ON EXTENDED MIXED NETW...cscpconf
The problem of finding maximum flow in network graph is extremely interesting and
practically applicable in many fields in our daily life, especially in transportation. Therefore, a
lot of researchers have been studying this problem in various methods. Especially in 2013, we
has developed a new algorithm namely, postflow-pull algorithm to find the maximum flow on
traditional networks. In this paper, we revised postflow-push methods to solve this
problem of finding maximum flow on extended mixed network. In addition, to take more
advantage of multi-core architecture of the parallel computing system, we build this
parallel algorithm. This is a completely new method not being announced in the world. The
results of this paper are basically systematized and proven. The idea of this algorithm is using
multi processors to work in parallel by postflow_push algorithm. Among these processors,
there is one main processor managing data, sending data to the sub processors, receiving data
from the sub-processors. The sub-processors simultaneously execute their work and send their
data to the main processor until the job is finished, the main processor will show the results of
the problem.
An Ant Algorithm for Solving QoS Multicast Routing ProblemCSCJournals
Abstract: Many applications require send information from a source to multiple destinations through a communication network. To support these applications, it is necessary to determine a multicast tree of minimal cost to connect the source node to the destination nodes subject to delay constraints. Based on the Ant System algorithm, we present an ant algorithm to find the multicast tree that minimizes the total cost. In the proposed algorithm, the k shortest paths from the source node to the destination nodes are used for genotype representation. The expermintal results show that the algorithm can find optimal solution quickly and has a good scalability.
In this paper, we solve this problem of finding maximum flow in extended mixed network by Revisedpreflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15]
In this paper, we solve this problem of finding maximum flow in extended mixed network by Revised preflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15].
In this paper, we solve this problem of finding maximum flow in extended mixed network by Revised preflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15].
ON THE IMPLEMENTATION OF GOLDBERG'S MAXIMUM FLOW ALGORITHM IN EXTENDED MIXED ...ijcsit
In this paper, we solve this problem of finding maximum flow in extended mixed network by Revised
preflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15].
However, we share some common theory with [15].
AMTR: THE ANT BASED QOS AWARE MULTIPATH TEMPORALLY ORDERED ROUTING ALGORITHM ...cscpconf
Mobile Ad hoc networks (MANETs) are self organized by a collection of mobile nodes, which are interconnected by multi hop wireless paths. Providing QoS support in MANETs is an active research area, basically for supporting real time applications that are based upon interaction between the routing scheme and QoS provisioning. The goal of QoS aware routing is to achieve more deterministic behavior of the network i.e. a stable path, so that information carried by the network can be delivered in an uninterrupted fashion and for better resource utilization. In this paper we have developed AMTR, a new ant based QoS aware on-demand multipath routing algorithm for MANETs with better route failure management and which will be highly adaptive and energy efficient.
Amtr the ant based qos aware multipath temporally ordered routing algorithm ...csandit
Mobile Ad hoc networks (MANETs) are self organized by a collection of mobile nodes, which
are interconnected by multi hop wireless paths. Providing QoS support in MANETs is an active
research area, basically for supporting real time applications that are based upon interaction
between the routing scheme and QoS provisioning. The goal of QoS aware routing is to achieve
more deterministic behavior of the network i.e. a stable path, so that information carried by the
network can be delivered in an uninterrupted fashion and for better resource utilization. In this
paper we have developed AMTR, a new ant based QoS aware on-demand multipath routing
algorithm for MANETs with better route failure management and which will be highly adaptive
and energy efficient.
To mine out relevant facts at the time of need from web has been a tenuous task. Research on diverse fields are fine tuning methodologies toward these goals that extracts the best of information relevant to the users search query. In the proposed methodology discussed in this paper find ways to ease the search complexity tackling the severe issues hindering the performance of traditional approaches in use. The proposed methodology find effective means to find all possible semantic relatable frequent sets with FP Growth algorithm. The outcome of which is the further source of fuel for Bio inspired Fuzzy PSO to find the optimal attractive points for the web documents to get clustered meeting the requirement of the search query without losing the relevance. On the whole the proposed system optimizes the objective function of minimizing the intra cluster differences and maximizes the inter cluster distances along with retention of all possible relationships with the search context intact. The major contribution being the system finds all possible combinations matching the user search transaction and thereby making the system more meaningful. These relatable sets form the set of particles for Fuzzy Clustering as well as PSO and thus being unbiased and maintains a innate behaviour for any number of new additions to follow the herd behaviour’s evaluations reveals the proposed methodology fares well as an optimized and effective enhancements over the conventional approaches
Improving initial generations in pso algorithm for transportation network des...ijcsit
Transportation Network Design Problem (TNDP) aims to select the best project sets among a number of new projects. Recently, metaheuristic methods are applied to solve TNDP in the sense of finding better solutions sooner. PSO as a metaheuristic method is based on stochastic optimization and is a parallel revolutionary computation technique. The PSO system initializes with a number of random solutions and seeks for optimal solution by improving generations. This paper studies the behavior of PSO on account of improving initial generation and fitness value domain to find better solutions in comparison with previous attempts.
Multi – Objective Two Stage Fuzzy Transportation Problem with Hexagonal Fuzzy...IJERA Editor
Fuzzy geometric programming approach is used to determine the optimal solution of a multi-objective two stage fuzzy transportation problem in which supplies, demands are hexagonal fuzzy numbers and fuzzy membership of the objective function is defined. This paper aims to find out the best compromise solution among the set of feasible solutions for the multi-objective two stage transportation problem. To illustrate the proposed method, example is used
Vehicle Ad Hoc Networks (VANETs) have become a viable technology to improve traffic flow and safety on the roads. Due to its effectiveness and scalability, the Wingsuit Search-based Optimised Link State Routing Protocol (WS-OLSR) is frequently used for data distribution in VANETs. However, the selection of MultiPoint Relays (MPRs) plays a pivotal role in WS-OLSR's performance. This paper presents an improved MPR selection algorithm tailored to WS-OLSR, designed to enhance the overall routing efficiency and reduce overhead. The analysis found that the current OLSR protocol has problems such as redundancy of HELLO and TC message packets or failure to update routing information in time, so a WS-OLSR routing protocol based on improved-MPR selection algorithm was proposed. Firstly, factors such as node mobility and link changes are comprehensively considered to reflect network topology changes, and the broadcast cycle of node HELLO messages is controlled through topology changes. Secondly, a new MPR selection algorithm is proposed, considering link stability issues and nodes. Finally, evaluate its effectiveness in terms of packet delivery ratio, end-to-end delay, and control message overhead. Simulation results demonstrate the superior performance of our improved MR selection algorithm when compared to traditional approaches.
A Novel Medium Access Control Strategy for Heterogeneous Traffic in Wireless ...IJCNCJournal
So far, Wireless Body Area Networks (WBANs) have played a pivotal role in driving the development of intelligent healthcare systems with broad applicability across various domains. Each WBAN consists of one or more types of sensors that can be embedded in clothing, attached directly to the body, or even implanted beneath an individual's skin. These sensors typically serve asingle application. However, the traffic generated by each sensor may have distinct requirements. This diversity necessitates a dual approach: tailored treatment based on the specific needs of each traffic typeand the fulfillment of application requirements, such asreliability and timeliness. Never the less, the presence of energy constraints and the unreliable nature of wireless communications make QoS provisioning under such networks a non-trivial task. In this context, the current paper introduces a novel Medium AccessControl (MAC) strategy for the regular traffic applications of WBANs, designed to significantly enhance efficiency when compared to the established MAC protocols IEEE 802.15.4 and IEEE 802.15.6, with a particular focus on improving reliability, timeliness, and energy efficiency.
May_2024 Top 10 Read Articles in Computer Networks & Communications.pdfIJCNCJournal
The International Journal of Computer Networks & Communications (IJCNC) is a bi monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Computer Networks & Communications. The journal focuses on all technical and practical aspects of Computer Networks & data Communications. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on advanced networking concepts and establishing new collaborations in these areas.
A Topology Control Algorithm Taking into Account Energy and Quality of Transm...IJCNCJournal
The efficient use of energy in wireless sensor networks is critical for extending node lifetime. The network topology is one of the factors that have a significant impact on the energy usage at the nodes and the quality of transmission (QoT) in the network. We propose a topology control algorithm for software-defined wireless sensor networks (SDWSNs) in this paper. Our method is to formulate topology control algorithm as a nonlinear programming (NP) problem with the objective to optimizing two metrics, maximum communication range, and desired degree. This NP problem is solved at the SDWSN controller by employing the genetic algorithm (GA) to determine the best topology. The simulation results show that the proposed algorithm outperforms the MaxPower algorithm in terms of average node degree and energy expansion ratio.
Multi-Server user Authentication Scheme for Privacy Preservation with Fuzzy C...IJCNCJournal
The integration of artificial intelligence technology with a scalable Internet of Things (IoT) platform facilitates diverse smart communication services, allowing remote users to access services from anywhere at any time. The multi-server environment within IoT introduces a flexible security service model, enabling users to interact with any server through a single registration. To ensure secure and privacy preservation services for resources, an authentication scheme is essential. Zhao et al. recently introduced a user authentication scheme for the multi-server environment, utilizing passwords and smart cards, claiming resilience against well-known attacks. This paper conducts cryptanalysis on Zhao et al.'s scheme, focusing on denial of service and privacy attacks, revealing a lack of user-friendliness. Subsequently, we propose a new multi-server user authentication scheme for privacy preservation with fuzzy commitment over the IoT environment, addressing the shortcomings of Zhao et al.'s scheme. Formal security verification of the proposed scheme is conducted using the ProVerif simulation tool. Through both formal and informal security analyses, we demonstrate that the proposed scheme is resilient against various known attacks and those identified in Zhao et al.'s scheme.
Advanced Privacy Scheme to Improve Road Safety in Smart Transportation SystemsIJCNCJournal
In -Vehicle Ad-Hoc Network (VANET), vehicles continuously transmit and receive spatiotemporal data with neighboring vehicles, thereby establishing a comprehensive 360-degree traffic awareness system. Vehicular Network safety applications facilitate the transmission of messages between vehicles that are near each other, at regular intervals, enhancing drivers' contextual understanding of the driving environment and significantly improving traffic safety. Privacy schemes in VANETs are vital to safeguard vehicles’ identities and their associated owners or drivers. Privacy schemes prevent unauthorized parties from linking the vehicle's communications to a specific real-world identity by employing techniques such as pseudonyms, randomization, or cryptographic protocols. Nevertheless, these communications frequently contain important vehicle information that malevolent groups could use to Monitor the vehicle over a long period. The acquisition of this shared data has the potential to facilitate the reconstruction of vehicle trajectories, thereby posing a potential risk to the privacy of the driver. Addressing the critical challenge of developing effective and scalable privacy-preserving protocols for communication in vehicle networks is of the highest priority. These protocols aim to reduce the transmission of confidential data while ensuring the required level of communication. This paper aims to propose an Advanced Privacy Vehicle Scheme (APV) that periodically changes pseudonyms to protect vehicle identities and improve privacy. The APV scheme utilizes a concept called the silent period, which involves changing the pseudonym of a vehicle periodically based on the tracking of neighboring vehicles. The pseudonym is a temporary identifier that vehicles use to communicate with each other in a VANET. By changing the pseudonym regularly, the APV scheme makes it difficult for unauthorized entities to link a vehicle's communications to its real-world identity. The proposed APV is compared to the SLOW, RSP, CAPS, and CPN techniques. The data indicates that the efficiency of APV is a better improvement in privacy metrics. It is evident that the AVP offers enhanced safety for vehicles during transportation in the smart city.
April 2024 - Top 10 Read Articles in Computer Networks & CommunicationsIJCNCJournal
The International Journal of Computer Networks & Communications (IJCNC) is a bi monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Computer Networks & Communications. The journal focuses on all technical and practical aspects of Computer Networks & data Communications. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on advanced networking concepts and establishing new collaborations in these areas.
DEF: Deep Ensemble Neural Network Classifier for Android Malware DetectionIJCNCJournal
Malware is one of the threats to security of computer networks and information systems. Since malware instances are available sufficiently, there is increased interest among researchers on usage of Artificial Intelligence (AI). Of late AI-enabled methods such as machine learning (ML) and deep learning paved way for solving many real-world problems. As it is a learning-based approach, accumulated training samples help in improving thequality of training and thus leveraging malware detection accuracy. Existing deep learning methods are focusing on learning-based malware detection systems. However, there is need for improving the state of the art through ensemble approach. Towards this end, in this paper we proposed a framework known as Deep Ensemble Framework (DEF) for automatic malware detection. The framework obtains features from training samples. From given malware instance a grayscale image is generated. There is another process to extract the opcode sequences. Convolutional Neural Network (CNN) and Long Short Term Memory (LSTM) techniques are used to obtain grayscale image and opcode sequence respectively. Afterwards, a stacking ensemble is employed in order to achieve efficient malware detection and classification. Malware samples collected fromthe Internet sources and Microsoft are used for theempirical study. An algorithm known as Ensemble Learning for Automatic Malware Detection (EL-AML) is proposed to realize our framework. Another algorithm named Pre-Process is proposed to assist the EL-AML algorithm for obtaining intermediate features required by CNN and LSTM.Empirical study reveals that our framework outperforms many existing methods in terms of speed-up and accuracy.
High Performance NMF Based Intrusion Detection System for Big Data IOT TrafficIJCNCJournal
With the emergence of smart devices and the Internet of Things (IoT), millions of users connected to the network produce massive network traffic datasets. These vast datasets of network traffic, Big Data are challenging to store, deal with and analyse using a single computer. In this paper we developed parallel implementation using a High Performance Computer (HPC) for the Non-Negative Matrix Factorization technique as an engine for an Intrusion Detection System (HPC-NMF-IDS). The large IoT traffic datasets of order of millions samples are distributed evenly on all the computing cores for both storage and speedup purpose. The distribution of computing tasks involved in the Matrix Factorization takes into account the reduction of the communication cost between the computing cores. The experiments we conducted on the proposed HPC-IDS-NMF give better results than the traditional ML-based intrusion detection systems. We could train the HPC model with datasets of one million samples in only 31 seconds instead of the 40 minutes using one processor), that is a speed up of 87 times. Moreover, we have got an excellent detection accuracy rate of 98% for KDD dataset.
A Novel Medium Access Control Strategy for Heterogeneous Traffic in Wireless ...IJCNCJournal
So far, Wireless Body Area Networks (WBANs) have played a pivotal role in driving the development of intelligent healthcare systems with broad applicability across various domains. Each WBAN consists of one or more types of sensors that can be embedded in clothing, attached directly to the body, or even implanted beneath an individual's skin. These sensors typically serve asingle application. However, the traffic generated by each sensor may have distinct requirements. This diversity necessitates a dual approach: tailored treatment based on the specific needs of each traffic typeand the fulfillment of application requirements, such asreliability and timeliness. Never the less, the presence of energy constraints and the unreliable nature of wireless communications make QoS provisioning under such networks a non-trivial task. In this context, the current paper introduces a novel Medium AccessControl (MAC) strategy for the regular traffic applications of WBANs, designed to significantly enhance efficiency when compared to the established MAC protocols IEEE 802.15.4 and IEEE 802.15.6, with a particular focus on improving reliability, timeliness, and energy efficiency.
A Topology Control Algorithm Taking into Account Energy and Quality of Transm...IJCNCJournal
The efficient use of energy in wireless sensor networks is critical for extending node lifetime. The network topology is one of the factors that have a significant impact on the energy usage at the nodes and the quality of transmission (QoT) in the network. We propose a topology control algorithm for software-defined wireless sensor networks (SDWSNs) in this paper. Our method is to formulate topology control algorithm as a nonlinear programming (NP) problem with the objective to optimizing two metrics, maximum communication range, and desired degree. This NP problem is solved at the SDWSN controller by employing the genetic algorithm (GA) to determine the best topology. The simulation results show that the proposed algorithm outperforms the MaxPower algorithm in terms of average node degree and energy expansion ratio.
Multi-Server user Authentication Scheme for Privacy Preservation with Fuzzy C...IJCNCJournal
The integration of artificial intelligence technology with a scalable Internet of Things (IoT) platform facilitates diverse smart communication services, allowing remote users to access services from anywhere at any time. The multi-server environment within IoT introduces a flexible security service model, enabling users to interact with any server through a single registration. To ensure secure and privacy preservation services for resources, an authentication scheme is essential. Zhao et al. recently introduced a user authentication scheme for the multi-server environment, utilizing passwords and smart cards, claiming resilience against well-known attacks. This paper conducts cryptanalysis on Zhao et al.'s scheme, focusing on denial of service and privacy attacks, revealing a lack of user-friendliness. Subsequently, we propose a new multi-server user authentication scheme for privacy preservation with fuzzy commitment over the IoT environment, addressing the shortcomings of Zhao et al.'s scheme. Formal security verification of the proposed scheme is conducted using the ProVerif simulation tool. Through both formal and informal security analyses, we demonstrate that the proposed scheme is resilient against various known attacks and those identified in Zhao et al.'s scheme.
Advanced Privacy Scheme to Improve Road Safety in Smart Transportation SystemsIJCNCJournal
In -Vehicle Ad-Hoc Network (VANET), vehicles continuously transmit and receive spatiotemporal data with neighboring vehicles, thereby establishing a comprehensive 360-degree traffic awareness system. Vehicular Network safety applications facilitate the transmission of messages between vehicles that are near each other, at regular intervals, enhancing drivers' contextual understanding of the driving environment and significantly improving traffic safety. Privacy schemes in VANETs are vital to safeguard vehicles’ identities and their associated owners or drivers. Privacy schemes prevent unauthorized parties from linking the vehicle's communications to a specific real-world identity by employing techniques such as pseudonyms, randomization, or cryptographic protocols. Nevertheless, these communications frequently contain important vehicle information that malevolent groups could use to Monitor the vehicle over a long period. The acquisition of this shared data has the potential to facilitate the reconstruction of vehicle trajectories, thereby posing a potential risk to the privacy of the driver. Addressing the critical challenge of developing effective and scalable privacy-preserving protocols for communication in vehicle networks is of the highest priority. These protocols aim to reduce the transmission of confidential data while ensuring the required level of communication. This paper aims to propose an Advanced Privacy Vehicle Scheme (APV) that periodically changes pseudonyms to protect vehicle identities and improve privacy. The APV scheme utilizes a concept called the silent period, which involves changing the pseudonym of a vehicle periodically based on the tracking of neighboring vehicles. The pseudonym is a temporary identifier that vehicles use to communicate with each other in a VANET. By changing the pseudonym regularly, the APV scheme makes it difficult for unauthorized entities to link a vehicle's communications to its real-world identity. The proposed APV is compared to the SLOW, RSP, CAPS, and CPN techniques. The data indicates that the efficiency of APV is a better improvement in privacy metrics. It is evident that the AVP offers enhanced safety for vehicles during transportation in the smart city.
DEF: Deep Ensemble Neural Network Classifier for Android Malware DetectionIJCNCJournal
Malware is one of the threats to security of computer networks and information systems. Since malware instances are available sufficiently, there is increased interest among researchers on usage of Artificial Intelligence (AI). Of late AI-enabled methods such as machine learning (ML) and deep learning paved way for solving many real-world problems. As it is a learning-based approach, accumulated training samples help in improving thequality of training and thus leveraging malware detection accuracy. Existing deep learning methods are focusing on learning-based malware detection systems. However, there is need for improving the state of the art through ensemble approach. Towards this end, in this paper we proposed a framework known as Deep Ensemble Framework (DEF) for automatic malware detection. The framework obtains features from training samples. From given malware instance a grayscale image is generated. There is another process to extract the opcode sequences. Convolutional Neural Network (CNN) and Long Short Term Memory (LSTM) techniques are used to obtain grayscale image and opcode sequence respectively. Afterwards, a stacking ensemble is employed in order to achieve efficient malware detection and classification. Malware samples collected fromthe Internet sources and Microsoft are used for theempirical study. An algorithm known as Ensemble Learning for Automatic Malware Detection (EL-AML) is proposed to realize our framework. Another algorithm named Pre-Process is proposed to assist the EL-AML algorithm for obtaining intermediate features required by CNN and LSTM.Empirical study reveals that our framework outperforms many existing methods in terms of speed-up and accuracy.
High Performance NMF based Intrusion Detection System for Big Data IoT TrafficIJCNCJournal
With the emergence of smart devices and the Internet of Things (IoT), millions of users connected to the network produce massive network traffic datasets. These vast datasets of network traffic, Big Data are challenging to store, deal with and analyse using a single computer. In this paper we developed parallel implementation using a High Performance Computer (HPC) for the Non-Negative Matrix Factorization technique as an engine for an Intrusion Detection System (HPC-NMF-IDS). The large IoT traffic datasets of order of millions samples are distributed evenly on all the computing cores for both storage and speedup purpose. The distribution of computing tasks involved in the Matrix Factorization takes into account the reduction of the communication cost between the computing cores. The experiments we conducted on the proposed HPC-IDS-NMF give better results than the traditional ML-based intrusion detection systems. We could train the HPC model with datasets of one million samples in only 31 seconds instead of the 40 minutes using one processor), that is a speed up of 87 times. Moreover, we have got an excellent detection accuracy rate of 98% for KDD dataset.
IoT Guardian: A Novel Feature Discovery and Cooperative Game Theory Empowered...IJCNCJournal
Cyber intrusion attacks increasingly target the Internet of Things (IoT) ecosystem, exploiting vulnerable devices and networks. Malicious activities must be identified early to minimize damage and mitigate threats. Using actual benign and attack traffic from the CICIoT2023 dataset, this WORK aims to evaluate and benchmark machine-learning techniques for IoT intrusion detection. There are four main phases to the system. First, the CICIoT2023 dataset is refined to remove irrelevant features and clean up missing and duplicate data. The second phase employs statistical models and artificial intelligence to discover novel features. The most significant features are then selected in the third phase based on cooperative game theory. Using the original CICIoT2023 dataset and a dataset containing only novel features, we train and evaluate a variety of machine learning classifiers. On the original dataset, Random Forest achieved the highest accuracy of 99%. Still, with novel features, Random Forest's performance dropped only slightly (96%) while other models achieved significantly lower accuracy. As a whole, the work contributes substantial contributions to tailored feature engineering, feature selection, and rigorous benchmarking of IoT intrusion detection techniques. IoT networks and devices face continuously evolving threats, making it necessary to develop robust intrusion detection systems.
Enhancing Traffic Routing Inside a Network through IoT Technology & Network C...IJCNCJournal
IoT networking uses real items as stationary or mobile nodes. Mobile nodes complicate networking. Internet of Things (IoT) networks have a lot of control overhead messages because devices are mobile. These signals are generated by the constant flow of control data as such device identity, geographical positioning, node mobility, device configuration, and others. Network clustering is a popular overhead communication management method. Many cluster-based routing methods have been developed to address system restrictions. Node clustering based on the Internet of Things (IoT) protocol, may be used to cluster all network nodes according to predefined criteria. Each cluster will have a Smart Designated Node. SDN cluster management is efficient. Many intelligent nodes remain in the network. The network design spreads these signals. This paper presents an intelligent and responsive routing approach for clustered nodes in IoT networks. An existing method builds a new sub-area clustered topology. The Nodes Clustering Based on the Internet of Things (NCIoT) method improves message transmission between any two nodes. This will facilitate the secure and reliable interchange of healthcare data between professionals and patients. NCIoT is a system that organizes nodes in the Internet of Things (IoT) by grouping them together based on their proximity. It also picks SDN routes for these nodes. This approach involves selecting one option from a range of choices and preparing for likely outcomes problem addressing limitations on activities is a primary focus during the review process. Predictive inquiry employs the process of analyzing data to forecast and anticipate future events. This document provides an explanation of compact units. The Predictive Inquiry Small Packets (PISP) improved its backup system and partnered with SDN to establish a routing information table for each intelligent node, resulting in higher routing performance. Both principal and secondary roads are available for use. The simulation findings indicate that NCIoT algorithms outperform CBR protocols. Enhancements lead to a substantial 78% boost in network performance. In addition, the end-to-end latency dropped by 12.5%. The PISP methodology produces 5.9% more inquiry packets compared to alternative approaches. The algorithms are constructed and evaluated against academic ones.
IoT Guardian: A Novel Feature Discovery and Cooperative Game Theory Empowered...IJCNCJournal
Cyber intrusion attacks increasingly target the Internet of Things (IoT) ecosystem, exploiting vulnerable devices and networks. Malicious activities must be identified early to minimize damage and mitigate threats. Using actual benign and attack traffic from the CICIoT2023 dataset, this WORK aims to evaluate and benchmark machine-learning techniques for IoT intrusion detection. There are four main phases to the system. First, the CICIoT2023 dataset is refined to remove irrelevant features and clean up missing and duplicate data. The second phase employs statistical models and artificial intelligence to discover novel features. The most significant features are then selected in the third phase based on cooperative game theory. Using the original CICIoT2023 dataset and a dataset containing only novel features, we train and evaluate a variety of machine learning classifiers. On the original dataset, Random Forest achieved the highest accuracy of 99%. Still, with novel features, Random Forest's performance dropped only slightly (96%) while other models achieved significantly lower accuracy. As a whole, the work contributes substantial contributions to tailored feature engineering, feature selection, and rigorous benchmarking of IoT intrusion detection techniques. IoT networks and devices face continuously evolving threats, making it necessary to develop robust intrusion detection systems.
** Connect, Collaborate, And Innovate: IJCNC - Where Networking Futures Take ...IJCNCJournal
The International Journal of Computer Networks & Communications (IJCNC) is a bi monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of Computer Networks & Communications. The journal focuses on all technical and practical aspects of Computer Networks & data Communications. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on advanced networking concepts and establishing new collaborations in these areas.
Enhancing Traffic Routing Inside a Network through IoT Technology & Network C...IJCNCJournal
IoT networking uses real items as stationary or mobile nodes. Mobile nodes complicate networking. Internet of Things (IoT) networks have a lot of control overhead messages because devices are mobile. These signals are generated by the constant flow of control data as such device identity, geographical positioning, node mobility, device configuration, and others. Network clustering is a popular overhead communication management method. Many cluster-based routing methods have been developed to address system restrictions. Node clustering based on the Internet of Things (IoT) protocol, may be used to cluster all network nodes according to predefined criteria. Each cluster will have a Smart Designated Node. SDN cluster management is efficient. Many intelligent nodes remain in the network. The network design spreads these signals. This paper presents an intelligent and responsive routing approach for clustered nodes in IoT networks. An existing method builds a new sub-area clustered topology. The Nodes Clustering Based on the Internet of Things (NCIoT) method improves message transmission between any two nodes. This will facilitate the secure and reliable interchange of healthcare data between professionals and patients. NCIoT is a system that organizes nodes in the Internet of Things (IoT) by grouping them together based on their proximity. It also picks SDN routes for these nodes. This approach involves selecting one option from a range of choices and preparing for likely outcomes problem addressing limitations on activities is a primary focus during the review process. Predictive inquiry employs the process of analyzing data to forecast and anticipate future events. This document provides an explanation of compact units. The Predictive Inquiry Small Packets (PISP) improved its backup system and partnered with SDN to establish a routing information table for each intelligent node, resulting in higher routing performance. Both principal and secondary roads are available for use. The simulation findings indicate that NCIoT algorithms outperform CBR protocols. Enhancements lead to a substantial 78% boost in network performance. In addition, the end-to-end latency dropped by 12.5%. The PISP methodology produces 5.9% more inquiry packets compared to alternative approaches. The algorithms are constructed and evaluated against academic ones.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
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
Antifertility, Toxicity studies as per OECD guidelines
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
EXTENDED LINEAR MULTI-COMMODITY MULTICOST NETWORK AND MAXIMAL FLOW LIMITED COST PROBLEMS
1. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
DOI: 10.5121/ijcnc.2018.10106 79
EXTENDED LINEAR MULTI-COMMODITY MULTI-
COST NETWORK AND MAXIMAL FLOW LIMITED
COST PROBLEMS
Tran Quoc Chien1
and Ho Van Hung2
1
The University of Education, University of Danang, Danang, Vietnam
2
Quangnam University, Tamky, Vietnam
ABSTRACT
The Graph is a powerful mathematical tool applied in many fields as transportation, communication,
informatics, economy, … In an ordinary graph, the weights of edges and vertexes are considered
independently where the length of a path is the sum of weights of the edges and the vertexes on this path.
However, in many practical problems, weights at a vertex are not the same for all paths passing this vertex
but depend on coming and leaving edges. The presented paper develops a model of the extended linear
multi-commodity multi-cost network that can be more exactly and effectively applied to model many
practical problems. Then, maximal limit cost flow problems are modeled as implicit linear programming
problems. On the base of dual theory in linear programming, an effective approximate algorithm is
developed.
KEYWORDS
Graph, Network, Multi-commodity Multi-cost Flow, Optimization, Linear-Programming.
1. INTRODUCTION
Network and its flow is a powerful mathematical tool applied in many fields as transportation,
communications, informatics, economics, and so on. So far, most of the applications in the new
graph solely considers to the weight of edges and nodes independently, in which the path length
merely is the sum of weights of edges and nodes along the path. However, in many practical
problems, the weight at one node is not the same for all paths passing through that node, but also
depends on coming and leaving edges. For example, the transit time on the transport network
depends on the direction of transportation: turn right, turn left or go straight, even some directions
are forbidden. Paper [2] proposes switching cost only for directed graphs. Therefore, it is
necessary to build an extended mixed network model in order to apply more accurate and
effective modeling of practical problems. Multi-commodity flow in traditional network problems
have been studied in the papers [1,3,4,5,6]. Multi-commodity flow in extended network problems
with extended transport networks were studied in the papers [7-11]. The paper[12] studies
maximal multi-commodity multi-cost flow problems.
The paper builds the extended multi-cost multi-commodity model in sections 2 and 3 to enable
modeling of more accurate and efficient real problems. Next, in section 4, the maximal limit cost
multi-commodity multi-cost flow problem is defined by a hidden linear programming problem
model. Based on the duality theory of linear programming, an approximation algorithm with
polynomial complexity is developed in section 5.
2. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
80
2. EXTENDED LINEAR MULTI-COMMODITY MULTI-COST NETWORK
Given mixed graph G = (V, E) with node set V and edge set E. The edges may be undirected or
directed. The symbol Ev is the set of edges incident vertice v∈V. There are many kinds of goods
circulating on the network. Commodities share the capacities of the edges, but have different
costs. The undirected edges represent the two-way edge, in which the goods on the same edge,
but reverse directions share the capacity of the edge.
The symbol r is the commodity number, qi> 0 is the coefficient of conversion of goods i, i =1..r.
Given the following functions:
Edge passing capacity function ce:E→R*
, where ce(e) is the passing capability of the edge e∈E.
Edge service coefficient function ze:E→R*
, where ze(e) is the passing ratio of the edge e∈E (the
real capacity of the edge e is ze(e).ce(e)).
Node passing capability function cv:V→R*
, where cv(u) is the passing capability of the node
u∈V .
Node service coefficient function zv:V→R*
, where zv(u) is the passing ratio of the node v∈V (the
real capacity of the node v is zv(v).cv(v)).
The tuples (V, E , ce, ze, cv, zv) are called extended networks.
Edge cost function i, i=1..r, bei:E→R*
, where bei(e) is the cost of passing e a converted unit of
commodity of type i. Note that with 2-way paths, the cost of each way may vary.
Node switch cost function i, i=1..r, bvi:V×Ev×Ev→R*
, where bvi(u,e,e’) is the cost of transferring a
converted unit of commodity of type i from edge e through u to edge e’.
The sets ((V, E, ce, ze, cv, zv,{bei,bvi, qi|i=1..r}) are called the extended linear multi-commodity
multi-cost network.
◊ Note: If bei(e)=∞, commodity of type i is prohibited from circulation on path e. If bvi(u,e,e’) =
∞, comodity of type i is banned from path e through u to path e’.
Let p be the path from node u to node v through edges ej, j=1..(h+1), and nodes uj, j=1..h as
follows
p = [u, e1, u1, e2, u2, …, eh, uh, eh+1, v]
The cost of circulating a converted unit of commodity of type i, i = 1..r, passing the path p, is
denoted by the symbol bi(p), and defined by the following formula:
bi(p) = ∑
+
=
1
1
)(
h
j
ji ebe + ∑=
+
h
j
jjji eeubv
1
1),,( (1)
3. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
81
3. MULTI-COMMODITY FLOW PROBLEMS IN EXTENDED LINEAR MULTI-
COMMODITY MULTI-COST NETWORK
Given a multi-cost multi-commodity network G=(V,E,ce, ze, cv, zv, {bei, bvi, qi|i=1..r}). Assume,
for each commodity of type i, i=1..r, there are ki source-target pairs (si,j, ti,j), j=1..ki, each pair
assigned a quantity of commodity of type i, that is necessary to move from source node si,j to
target node ti,j.
Denote Pi,j is the set of paths from node si,j to node ti, in G, which commodity of type i can be
passed, i=1..r, j=1..ki. Set
Pi = U
ik
j
jiP
1
,
=
. (2)
For each path p∈Pi,j, i=1..r, j=1..ki, denote xi,j(p) the flow of converted commodity of type i from
the source node si,j to the destination node ti,j along the path p, i=1..r, j=1..ki.
Denote Pi,e the set of paths in Pi passing through the edge e, ∀e∈E.
Denote Pi,v the set of paths in Pi passing through the node v, ∀v∈V.
A set
F = {xi,j(p) | p∈Pi,j, i=1..r, j=1..ki} (3)
is called a multi-commodity flow on the linear extended multi-commodity multi-cost network, if
it satisfies the following edge and node capacity constraints:
( )∑∑ ∑= = ∈
r
i
k
j Pp
ji
i
ei
px
1 1
,
,
≤ ce(e).ze(e), ∀e∈E
( )∑∑ ∑= = ∈
r
i
k
j Pp
ji
i
vi
px
1 1
,
,
≤ cv(v).zv(v), ∀v∈V
The expressions
fvi,j = ( )∑∈ jiPp
ji px
,
, ,i=1..r,j=1..ki (4)
is called the flow value of commodity of type i of the source-target pair (si,j,ti,j) of F.
The expressions
fvi = ∑=
ik
j
jifv
1
, , i=1..r (5)
is called the flow value of commodity of type i of F.
The expression
fv = ∑=
r
i
ifv
1
(6)
Allied the flow value of F.
4. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
82
4. MAXIMAL LIMITED COST MULTI-COMMODITY FLOW PROBLEMS
Given an extended linear multi-commodity multi-cost network G=(V,E, ce, ze, cv, zv, {bei, bvi,
qi|i=1..r}). Assume, for each commodity of type i, i=1..r, there are ki source-target pairs (si,j, ti,j),
j=1..ki, each pair assigned a quantity of commodity of type i, that is necessary to move from
source node si,j to target node ti,j. Given a limit cost B.
The task of the problem is to find the multi-commodity flow such that the value of the flow fv is
maximal. At the same time, the total cost of the flow does not exceed B.
The problem is expressed by an implicit linear programming model (P) as follows:
fv= ∑∑ ∑= = ∈
r
i
k
j Pp
ji
i
ji
px
1 1
,
,
)( →max
satisfies
( )∑∑ ∑= = ∈
r
i
k
j Pp
ji
i
ei
px
1 1
,
,
≤ ce(e).ze(e), ∀e∈E
( )∑∑ ∑= = ∈
r
i
k
j Pp
ji
i
vi
px
1 1
,
,
≤ cv(v).zv(v), ∀v∈V (P)
( ) )(.
1 1
,
,
pbpx i
r
i
k
j Pp
ji
i
ji
∑∑ ∑= = ∈
≤ B
xi,j(p) ≥0, ∀i=1..r, j=1..ki, ∀p∈Pi,j
The dual linear programming problem of (P), called (D), is constructed as follows: each edge
e∈E is assigned an dual variable le(e), each node v∈V is assigned an dual variable lv(v) while the
dual variable ϕ assigns the constraint of cost. The problem (D) states the following
D(le,lv,ϕ) = ( ) ( )∑∈Ee
eleezeece ).(. + ( ) ( )∑∈Vv
vlvvzvvcv ).(. + B.ϕ → min
( )∑∈pe
ele + ( )∑∈pv
vlv + bi(p).ϕ ≥ 1, ∀p∈Pi,j (D)
le(e) ≥ 0,∀e∈E, lv(v) ≥ 0,∀v∈V, ϕ ≥ 0
Now, given p∈Pi, i=1..r, a path from node u to node v through edges ej, j=1..(h+1), and nodes uj,
j=1..h, as follows
p = [u, e1, u1, e2, u2, …, eh, uh, eh+1, v]
We define the path length of p, denoted by lengthi(p), depending on the variables le(e), lv(v) and
ϕ so as to the following formula:
lengthi(p) = ∑
+
=
1
1
)(
h
j
jele +∑=
h
j
julv
1
)( + bi(p).ϕ (7)
5. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
83
Denote disti,j(le,lv,ϕ) the shortest path length from si,j to ti,j calculated by function lengthi(p),
∀i=1..r, ∀j=1..ki.
Set α(le,lv,ϕ) = min{disti,j(le,lv,ϕ) | i=1..r, j=1..ki}
Consider the problem (Dα):
β =
≥→→ 0,:,:
),,(
),,(
min **
ϕ
ϕα
ϕ
RVlvREle
lvle
lvleD
(8)
• Lemma 4.1. The problem (D) is equivalent to the problem (Dα) such that their optimal value
are equal and the optimal solution of one problem derives the optimal solution of the other
problem and vice versa.
Proof
Denote min(D) and min(Dα), respectively, the optimal values of the problem (D) and the problem
(Dα) . Given functions le: E→R*
, lv:V→R*
, ϕ > 0. Set
le’(e) = le(e)/α(le,lv,ϕ), ∀e∈E, lv’(v) = lv(v)/α(le,lv,ϕ), ∀v∈V, ϕ’ = ϕ/α(le,lv,ϕ). (9)
We have:
( )∑∈pe
ele' + ( )∑∈pv
vlv' +bi(p).ϕ’ ≥ 1,∀i=1..r, ∀j=1..ki, ∀p∈Pi,j (10)
So (le’,lv’,ϕ’) is an accepted solution of (D) and
D(le’,lv’,ϕ’) =
),,(
),,(
ϕα
ϕ
lvle
lvleD
. (11)
Hence inferred
min(D) ≤ min(Dα) (12)
In contrast, let (le,lv,ϕ) be an accepted solution of (D). Then, we have
1 ≤ disti,j(le,lv,ϕ), ∀i=1..r,∀j=1..ki ⇒ α(le,lv,ϕ) ≥ 1 ⇒
),,(
),,(
ϕα
ϕ
lvle
lvleD
≤ D(le,lv,ϕ).
Hence Inferred
min(D) ≥min(Dα) (13)
From (12) and (13), it follows min(D) = min(Dα).
Next, if (le,lv,ϕ) is an optimal solution of the problem (Dα), then (le’,lv’,ϕ’) where
le’(e) = le(e)/α(le,lv,ϕ), ∀e∈E, lv’(v) = lv(v)/α(le,lv,ϕ), ∀v∈V, ϕ’ = ϕ/α(le,lv,ϕ).
is an optimal solution of problem (D).
Conversely, if (le,lv,ϕ) is an optimal solution of the problem (D), then (le,lv,ϕ) is an optimal
solution of the problem (Dα).
6. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
84
5. ALGORITHM
• IDEAS
The algorithm consists of a number of iterative steps, through the function lengthi(p), p∈Pi,
i=1..r. At each iteration step, find the shortest path p, with respect to the length function
lengthi(p)) between the source-destination pairs and convert c units of exchange through p, where
c is the minimal edge and node capacity on this path.
Then change the value of functions le, lv and ϕ..The algorithm stops once α ≥ 1. The initial value
of le, lv and ϕ depends on the approximate value to be achieved.
• ALGORITHM
◊ INPUT: Extended multi-cost multi-commodity network G=(V,E, ce, ze, cv, zv, {bei, bvi,
qi|i=1..r}). Assume, for each commodity of type i, i=1..r, there are ki source-target pairs (si,j, ti,j),
j=1..ki, each pair assigned a quantity of commodity of type i, that is necessary to move from
source node si,j to target node ti,j. Given a limited cost B, an approximation ratio ω.
◊ OUTPUT : Maximal flow F represents a set of converged flows at the edges
F = {xi,j(e) | e∈E, i=1..r, j=1..ki}
with total cost not over the limit cost B.
◊ PROCEDURE
Note n=|V|, m=|E|, Bf total cost of the flows F.
Calculate bmin, the smallest cost in the paths from the source si,j to the destination ti,j, i=1..r,
j=1..ki :
bmin = min{bi(p) | i=1..r, j=1..ki, p∈Pi,j}. (14)
Calculate bmax, the largest cost of the paths from the source si,j to the destination ti,j, i=1..r, j=1..ki.
bmax = max{bi(p) | i=1..r, j=1..ki, p∈Pi,j}. (15)
Set
ε = 1− )1/(1 ω+ ; δ = (1+ε)
[ ] ε
ε
/12
min)max/()1(
1
bbnm +++
; (16)
for e∈E : le(e)=δ; xi,j(e)=0 ; for v∈V : lv(v)=δ ; (17)
ϕ = δ/bmin ; fv = 0; Bf = 0 ; (18)
do
{
Use the algorithm to find the source-destination pair (si,j, ti,j), 1≤i≤r and 1≤j≤ki, having the shortest
path from si,j to ti,j calculated by the length function lengthi(.).Note that the path p must be valid
7. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
85
for goods of type i, i.e., not containing the edge with edge cost ∞ or the node with the switch
cost∞.
Note
imin and jmin the indexes of source-destination pairs with the shortest path;
α is the shortest path length;
p is the shortest path;
c is the minimal edge and node capacity on the path p, i.e.
c=min{min{ce(e).ze(e)|e∈p},min{cv(v).zv(v)|v∈p}};
B’ = c.bimin(p);
if (B’>B){ c = c.B / B’; B’ = B; }
Flow adjustments:
∀e∈p, xi,j(e)=xi,j(e)+c;le(e)=le(e).(1+ε.c/(ce(e).ze(e))); (19)
∀v∈p, lv(v)=lv(v).(1+ε.c/(cv(v).zv(v))); (20)
ϕ = ϕ.(1+ε.B’/B) ; Bf = Bf + B’ ; fv = fv + c ; (21)
} while (α < 1)
Modifying the resulting flows F and flow value fv.
xi,j(e)=xi,j(e) /
δ
ε
ε
+
+
1
log1 ; ∀i=1..r, j=1..ki,∀e∈E; (22)
fv = fv /
δ
ε
ε
+
+
1
log1 ; Bf = Bf/
δε
1
log1+ ; (23)
Modifying flows on scalar edge
for (i=1 ; i<=r ;i++)
for (j=1 ; j<=ki ;j++)
for scalar e∈E
if xi,j(e) >= xi,j(e’)// e’ is the opposite of the direction e
{xi,j(e) = xi,j(e)−xi,j(e’) ; xi,j(e’)=0};
else
{xi,j(e’) = xi,j(e’)−xi,j(e) ; xi,j(e)=0};
• PROOF OF ALGORITHM
Denote
D(0) the initial value of function D
D(0) = ( )∑∈Ee
ezeece δ).(. + ( )∑∈Vv
vzvvcv δ).(. + B.δ/bmin
= δ.( ( )∑∈Ee
ezeece )(. + ( )∑∈Vv
vzvvcv )(. + B/bmin) (24)
D(i) is the value of the function D after the loop i, i=1, 2, ...
8. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
86
fv(0) = 0 is the initial value of the flow F.
fv(i) is the value of the flow F after the loop i, i=1, 2, ...
le0, lv0 and ϕ0 are, respectively, initial values of the functions le, lv and ϕ.
lei, lvi and ϕi correspond respectively to le, lv and ϕ in the loop i. i=1, 2, ...
pi is the shortest path p in the loop i. i=1, 2, ...
α(i)= α(lei,lvi,ϕi), i = 1, 2, ...
c(i) is the value of c in the loop i. i = 1, 2, ...
We have
fv(j) = fv(j−1) + c(j), (25)
D(j) = ( ) ( )∑∈Ee
j eleezeece ).(. + ( ) ( )∑∈Vv
j vlvvzvvcv ).(. + B.ϕj
= ( ) ( )∑∈
−
Ee
j eleezeece 1).(. + ( ) ( )∑∈
−
Vv
j vlvvzvvcv 1).(. +B.ϕj−1
+ ( )∑∈
−
jpe
j elejc 1)(.ε + ( )∑∈
−
jpv
j vlvjc 1)(.ε + ε.B’.ϕj−1
= D(j−1) + ε.c(j).( ( )∑∈
−
jpe
j ele 1 + ( )∑∈
−
jpv
j vlv 1 + bimin(pj-1).ϕj−1)
= D(j−1) + ε.c(j).α(j−1). (26)
It follows
D(i) = D(0)+ε ( )∑=
−−−
i
j
jjfvjfv
1
)1()1()( α , ∀i≥1 (27)
Consider functions lei−le0 và lvi−lv0 và ϕi−ϕ0. We have
D(lei−le0,lvi−lv0,ϕi−ϕ0) = D(i)– D(0). (28)
Next, consider α(lei−le0,lvi−lv0,ϕi−ϕ0). We have
α(le,lv,ϕ) = min{distg,l(le,lv,ϕ) | g=1..r, l=1..kg} (29)
and
distg,l(le,lv,ϕ)
= min{ ∑
+
=
1
1
)(
h
j
jele + ∑=
h
j
julv
1
)( + bg(p).ϕ|p = [si,j, e1, u1, e2, u2, …, eh, uh, eh+1,ti,j]∈Pg,l } (30)
Thus
distg,l(lei−le0,lvi−lv0,ϕi−ϕ0)
= min{ ( )∑
+
=
−
1
1
0 )()(
h
j
jj eleele + ( )∑=
−
h
j
jj ulvulv
1
0 )()( + bg(p).ϕi−bg(p).ϕ0
| p = [si,j, e1, u1, e2, u2, …, eh, uh, eh+1,ti,j]∈Pg,l } (31)
= min{∑
+
=
1
1
)(
h
j
ji ele + ∑=
h
j
ji ulv
1
)( + bg(p).ϕi−( ∑
+
=
1
1
0 )(
h
j
jele + ∑=
h
j
julv
1
0 )( +bg(p).ϕ0)
| p = [si,j, e1, u1, e2, u2, …, eh, uh, eh+1,ti,j]∈Pg,l } (32)
9. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
87
≥ min{ ∑
+
=
1
1
)(
h
j
ji ele + ∑=
h
j
ji ulv
1
)( + bg(p).ϕi−(m.δ+ n.δ +δ.bg(p)/bmin)
| p = [si,j, e1, u1, e2, u2, …, eh, uh, eh+1,ti,j]∈Pg,l } (33)
≥ min{ ∑
+
=
1
1
)(
h
j
ji ele + ∑=
h
j
ji ulv
1
)( + bg(p).ϕi−δ.(m + n +bmax/bmin)
| p = [si,j, e1, u1, e2, u2, …, eh, uh, eh+1,ti,j]∈Pg,l } (34)
= min{∑
+
=
1
1
)(
h
j
ji ele + ∑=
h
j
ji ulv
1
)( + bg(p).ϕi| p = [si,j, e1, u1, e2, u2, …, eh, uh, eh+1,ti,j]∈Pg,l}
−δ.(m + n +bmax/bmin) (35)
= distg,l(lei,lvi,ϕi)−δ.(m + n +bmax/bmin) (36)
Hence,
α.(lei−le0,lvi−lv0,ϕi−ϕ0) ≥ α(i)−δ.(m+n+bmax/bmin). (37)
Denote i0 the smallest index sastifies
α(i0) ≥ δ.(m+n+bmax/bmin) and α(i0−1) < δ.(m+n+bmax/bmin) (38)
On the other hand, we have
lei(e) ≤ lei−1(e).(1+ε.c(j) /(ce(e).ze(e))) ≤ lei−1(e).(1+ε), ∀e∈E, ∀i ≥ 1 (39)
lvi(v) ≤ lvi−1(v).(1+ε.c(j) /(cv(v).zv(v))) ≤ lvi−1(v).(1+ε), ∀v∈V, ∀i ≥ 1 (40)
and
ϕi = ϕi−1(1+ε.B’/ B) ≤ ϕi−1(1+ε), (41)
⇒ α(i) ≤ (1+ε).α(i−1), ∀i ≥ 1. (42)
It follows
α(i0) ≤ (1+ε).α(i0−1) < (1+ε).δ.(m+n+bmax/bmin) (43)
Then, we have
β ≤
( )
( )000
000
,,
,,
ϕϕα
ϕϕ
−−−
−−−
iii
iii
lvlvlele
lvlvleleD
≤
min)max/()(
)0()(
bbnmi
DiD
++−
−
δα
, ∀i ≥ i0 +1 (44)
Substituting D(i)–D(0) from (27) into (44), we obtain:
α(i) ≤ δ.(m+n+bmax/bmin) +
β
ε
( )∑=
−−−
i
j
jjfvjfv
1
)1()1()( α , ∀i ≥ i0 +1 (45)
We define x(i0), x(i0 +1), ..., x(i0 +i), ... as follows:
x(i0) = α(i0) và x(i) = δ.(m+n+bmax/bmin)+
β
ε
( )∑=
−−−
i
j
jxjfvjfv
1
)1()1()( , ∀i ≥i0+1 (46)
10. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
88
Inductively, it folows
α(i) ≤ x(i), ∀i ≥ i0 +1 (47)
We have
x(i) =δ.(m+n+bmax/bmin)+
β
ε
( )∑
−
=
−−−
1
1
)1()1()(
i
j
jxjfvjfv +
β
ε
(fv(i)−fv(i−1)).x(i−1) (48)
= x(i−1) (1+ε( fv(i)−fv(i−1))/β) ≤ x(i−1) ( ) βε /)1()( −− ifvifv
e ≤ x(i−2) ( ) βε /)2()( −− ifvifv
e ≤ … (49)
≤ x(i0) βε /))()(.( 0ifvifv
e −
≤ α(i0). βε /)(. ifv
e ≤ (1+ε).δ.(m+n+bmax/bmin) βε /)(. ifv
e , (50)
for α(i0) ≤ (1+ε).δ.(m+n+bmax/bmin).
It then follows
α(i) ≤ (1+ε).δ.(m+n+bmax/bmin) βε /)(. ifv
e , ∀I ≥ i0+1. (51)
Suppose the algorithm ends in the loop t, α(t) ≥ 1. Then
1 ≤ (1+ε).δ.(m+n+bmax/bmin) βε /)(. tfv
e (52)
that follows
)(tfv
β
≤
)bmax/bmin.().1(
1
ln
+++ nmδε
ε
(53)
Lemma 5.1. There exists an accepted flow with value
δ
ε
ε
+
+
1
log
)(
1
tfv
.
Proof. Consider any edge e. We have :
For each transfer of ce(e)ze(e) converted units of commodities through e, the length le(e) of e
increases by a factor ≥ (1+ε). Indeed, at each iteration we only transfer c≤ce(e)ze(e) converted
units of commodities through e. So, in order to transfer of ce(e)ze(e) converted units of
commodities through e, commodities must be transferred through e at least in one iteration.
Suppose it starts at iteration i. Let q be the number of iterations to transfer of ce(e)ze(e) converted
units of commodities through e. Denote cj the value of c at the j-th transfer through e, j=1..q.
Denote l the last iteration that transfers cq converted units of commodities through e. We have
lel(e) = lei(e).
+
)()(
.1 1
ezeece
c
ε …
+
)()(
.1
ezeec
cq
ε (54)
=lei(e). ( )
++++ ...
)()(
....1 1
ezeec
cc q
ε
(55)
Then, we have
∑=
q
j
jc
1
≥ ce(e)ze(e). (56)
Thus
11. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
89
lel(e) ≥ (1+ε).lei(e). (57)
Assumes x (e) be the sum of the flows through e. Set
x(e) = h.ce(e)ze(e), h∈R*
. (58)
So there are h times of ce(e)ze(e) unit of goods passes e, then the length of e is
let(e) ≥ (1+ε)h
.le0(e) (59)
Let j, j<t, be the last iteration of increasing le(e). Then lej(e) < 1, (for if lej(e) ≥ 1, then α(j)≥1,
and the algorithm stopped at step j<t). So,
let(e) ≤ (1+ε).lej(e) < (1+ε) (60)
From (59), (60) and le0(e)=δ it follows
(1+ε)h
.le0(e) ≤ let(e) < (1+ε) ⇒ h <
δ
ε
ε
+
+
1
log1 . (61)
So
x(e) ≤ ce(e)ze(e).
δ
ε
ε
+
+
1
log1 , ∀e∈E. (62)
Similarly, we also have
x(v) ≤ cv(v).zv(v).
δ
ε
ε
+
+
1
log1 , ∀v∈V (63)
where x(v) is the total converted units of commodities passing through the node v∈V.
Thus, divide all flows xi,j(e) by
δ
ε
ε
+
+
1
log1 :
xi,j(e) = xi,j(e)/
δ
ε
ε
+
+
1
log1 , ∀i=1..r, j=1..ki, ∀e∈E, (64)
we receive accepted flows, which satisfies the conditions of edge and node capacities, with the
flow value of
δ
ε
ε
+
+
1
log
)(
1
tfv
.
Lemma 5.2. Flow with value
δ
ε
ε
+
+
1
log
)(
1
tfv
is maximal with approximation ratio 1+ω.
Proof
Denote γ the ratio of the dual optimal value divided by the flow value of
{xi,j(e) | e∈E, i=1..r, j=1..ki }
We have
γ =
)(tfv
β
.
δ
ε
ε
+
+
1
log1 . (65)
Using (53) we have
12. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
90
γ≤
min)max/()1(
1
ln
bbnm +++ δε
ε
.
δ
ε
ε
+
+
1
log1 =
)1ln( ε
ε
+
.
min)max/()1(
1
ln
1
ln
bbnm +++
+
δε
δ
ε
. (66)
Select
δ = (1+ε)
[ ] ε
ε
/12
min)max/()1(
1
bbnm +++
. (67)
We have
min)max/()1(
1
ln
1
ln
bbnm +++
+
δε
δ
ε
= (1−ε)−1
(68)
⇒
γ ≤
( )( )2/.1 2
εεε
ε
−−
≤
( )2
1
1
ε−
(69)
So 1 < γ ≤
( )2
1
1
ε−
. In order to get approximation ratio (1+ω), we choose ε such that
( )2
1
1
ε−
≤≤≤≤ (1+ω). So, with 0 < ε ≤ 1− )1/(1 ω+ , the flow with value
δ
ε
ε
+
+
1
log
)(
1
tfv
is maximal at
approximation ratio 1+ω .
• Note. From the converting flows {xi,j(e) | e∈E, i=1..r, j=1..ki } we can deduce the actual flows
by dividing the converted flows xi,j(e) by the conversion factor qi,∀i=1..r, j=1..ki, ∀e∈E.
• Lemma 5.3. The total flow cost in t iterations does not exceed B.
δ
ε
ε
+
+
1
log1 . That is, the total
cost of the flow after divide by
δ
ε
ε
+
+
1
log1 does not exceed B.
Proof. We have ϕ0 = δ/bmin. After (t−1) iterations, we have α(t−1) <1, it mean
( )∑
−∈
−
1
1
tpe
t ele + ( )∑
−∈
−
1
1
tpv
t vlv + bimin(p−-1).ϕt−1 < 1 (70)
⇒ ϕt−1< 1/bimin(pt-1) ≤ 1/bmin. (71)
Furthermore, while transferring commodities on the networks makes the total cost increasing to
B, so that ϕ increases to a factor of not less than (1+ε). Thus, calling x is the number of times the
algorithm increases the cost per unit B in the t loop, we have ϕ0.(1+ε)x
≤ ϕt ≤ (1+ε).ϕt−1 ≤ (1+ε)
/bmin. Due ϕ0 = δ/bmin, it follows x ≤
δ
ε
ε
+
+
1
log1 .
13. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
91
So the total cost of the flows after t iterations does not exceed B.
δ
ε
ε
+
+
1
log1 . When dividing the
flow by
δ
ε
ε
+
+
1
log1 , we also have the total cost decreasing factor
δ
ε
ε
+
+
1
log1 to satisfy the
requirements of the problem.
6. ALGORITHM COMPLEXITY
Theorem 6.1. The algorithm has a complexity of
O(ω−2
.k.n3
.(m+n).ln(m+n+bmax/bmin)),
where k=k1+…+kr, m is the number of edges in the graph, n is the number of vertices.
Proof. Consider the iterations i. Suppose e is the edge capacity of passing the smallest
ce(e)ze(e)=c(i) along the shortest path pi. We increase the lei(e) of e factor (1+ε). Considering any
e, let te be the number of iterations in which e has minimal capacity on corresponding path. Since
le0(e) =δ and let(e) <1+ε, we have
le0(e).(1+ε)te
= δ.(1+ε)te
≤ let(e) < 1+ε, (72)
what follows te <
δ
ε
ε
+
+
1
log1 .
On the other hand,
δ = (1+ε)
[ ] ε
ε
/12
min)max/()1(
1
bbnm +++
(73)
⇒ te ≤
ε
1
(2+log1+ε(m+n+bmax/bmin)) (74)
≤
)1ln(.
1
εε +
(2ln(1+ε)+ln(m+n+bmax/bmin)). (75)
Set
t* =
)1ln(.
1
εε +
(2ln(1+ε)+ln(m+n+bmax/bmin)). (76)
Then, each edge e∈E corresponds to at most t* times of finding shortest paths.
Similarly, each node v∈V corresponds to at most t* times of finding shortest paths.
So the times of finding shortest paths ≤ (m+n).t*.
The algorithm that finds the shortest path between the two source-destination ends has a
complexity of O(n3
) [7, 8], which inferred the shortest path finding algorithm between k pairs of
destination source ends with complexity O(k.n3
). Inferring the complexity of the algorithm is
O(k.n3
).O((m+n).
)1ln(.
min)max/ln(
εε +
++ bbnm
) (77)
14. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
92
On the other hand, because of ε ≤ 1− )1/(1 ω+ , we have
ε.ln(1+ε) ≈ ε2
≤ (1− )1/(1 ω+ )2
= (1−(1−0.5ω+o(ω)))2
= O(ω2
) (78)
Finally, from (77) and (78) it deduce the complexity of the algorithm
O(ω−2
.k.n3
.(m+n).ln(m+n+bmax/bmin)).
7. CONCLUSIONS
The paper develops a model of extended linear multi-commodity multi-cost network that can be
more exactly and effectively applied to model many practical problems. Then, maximal limit cost
flow problems are modeled as implicit linear programming problems. On the base of dual theory
in linear programming an effective approximate algorithm is developed. Correctness and
algorithm complexity are justified. The results of this paper are the basis for studying the multi-
commodity multi-cost flow optimization problem.
At last we emphasis that there is no efficient method solving implicit linear problems. Otherwise,
it is almost impossible to present this problem as an explicit linear problem, for the number of all
paths p, which determines the variables x(p), is as big as O(nn
). So, in case this problem is
converted to an explicit linear problem and solved by any known method (f.e. simplex method),
the complexity is much bigger than O(nn
), that is not practically acceptable.
REFERENCES
[1] Naveen Garg, Jochen Könemann: Faster and Simpler Algorithms for Multicommodity Flow and
Other Fractional Packing Problems, SIAM J. Comput, Canada, 37(2), 2007, pp. 630-652.
[2] Xiaolong Ma, Jie Zhou: An Extended Shortest Path Problem with Switch Cost Between Arcs,
Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol
IIMECS 2008, 19-21 March, 2008, Hong Kong.
[3] Tran Quoc Chien: Linear multi-channel traffic network, Ministry of Science and Technology, code
B2010DN-03-52.
[4] Tran Quoc Chien, Tran Thi My Dung: Application of the shortest path finding algorithm to find the
maximum flow of goods. Journal of Science & Technology, University of Danang, 3 (44) 2011.
[5] Tran Quoc Chien: Application of the shortest multi-path finding algorithm to find the maximum
simultaneous flow of goods simultaneously. Journal of Science & Technology, University of Danang,
4 (53) 2012.
[6] Tran Quoc Chien: Application of the shortest multi-path finding algorithm to find the maximal
simultaneous flow of goods simultaneously the minimum cost. Journal of Science & Technology, Da
Nang University, 5 (54) 2012.
[7] Tran Quoc Chien: The algorithm finds the shortest path in the general graph, Journal of Science &
Technology, University of Da Nang, 12 (61) / 2012, 16-21.
[8] Tran Quoc Chien, Nguyen Mau Tue, Tran Ngoc Viet: The algorithm finds the shortest path on the
extended graph. Proceeding of the 6th National Conference on Fundamental and Applied Information
Technology (FAIR), Proceedings of the Sixth National Conference on Scientific Research and
Application, Hue, 20-21 June 2013. Publisher of Natural Science and Technology. Hanoi 2013.
p.522-527.
[9] Tran Quoc Chien: Applying the algorithm to find the fastest way to find the maximum linear and
simultaneous minimum cost on an extended transportation network, Journal of Science &
Technology, University of Da Nang . 10 (71) 2013, 85-91.
15. International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.1, January 2018
93
[10] Tran Ngoc Viet, Tran Quoc Chien, Nguyen Mau Tue: Optimized Linear Multiplexing Algorithm on
Expanded Transport Networks, Journal of Science & Technology, University of Da Nang. 3 (76)
2014, 121-124.
[11] Tran Ngoc Viet, Tran Quoc Chien, Nguyen Mau Tue: The problem of linear multi-channel traffic
flow in traffic network. Proceedings of the 7th National Conference on Fundamental and Applied
Information Technology Research (FAIR'7), ISBN: 978-604-913-300-8, Proceedings of the 7th
National Science Conference "Fundamental and Applied Research IT ", Thai Nguyen, 19-20 / 6/2014.
Publisher of Natural Science and Technology. Hanoi 2014. p.31-39.
[12] Tran Quoc Chien, Ho Van Hung: Extended linear multi-commodity multi-cost network and maximal
flow finding problem. FAIR-2017.
AUTHORS
Ass. Prof. DrSc. Tran Quoc Chien (http://scv.ued.udn.vn/ly_lich/chi_tiet/275).He
has 14 papers in SCIE of Journal (http://www.kybernetika.cz/contact.html). Born in
1953 in Dien Ban, Quang Nam, Vietnam. He graduated from Maths_IT faculty. He
got Ph.D Degree of maths in 1985 in Charles university of Prague, Czech Republic
and hold Doctor of Science in Charles university of Prague, Czech Republic in 1991.
He received the tittle of Ass. Pro in 1992. He work for university of Danang,
Vietnam. His main major: Maths and computing, applicable mathematics in
transport, maximum flow, parallel and distributed process, discrete mathemetics,
graph theory, grid Computing, distributed programming.
M.Si. Ho Van Hung (http://qnamuni.edu.vn/viewLLKH.asp?MaGV=134). Born in
1977 in Thang Binh, Quang Nam, Vietnam. He graduated from Faculty of Information
Technology – College of Sciences – Hue University in 2000. He got master of science
(IT) at Danang university of technology. His main major: Applicable mathematics in
transport, maximum flow, parallel and distributed process, graph theory and
distributed programming.