This document provides an overview and analysis of common group communication operations that are frequently used in parallel programs. It discusses efficient algorithms for one-to-all broadcast, all-to-one reduction, all-to-all broadcast, all-reduce, scatter, gather, and all-to-all personalized communication on different network topologies like rings, meshes, and hypercubes. It analyzes the time complexity of each algorithm and compares different approaches for each operation. The goal is to illustrate how to design efficient algorithms for these operations by leveraging the underlying network architecture.
Basic communication operations - One to all BroadcastRashiJoshi11
This document discusses one-to-all broadcast operations in parallel computing. It describes one-to-all broadcast, where a single process sends identical data to all other processes. It then discusses implementations of one-to-all broadcast on ring/linear array, mesh, and hypercube network topologies. It analyzes the time cost of one-to-all broadcast as O(logp) message transfers. It also describes how to improve the speed using a scatter-all-to-all broadcast approach for large messages.
This document discusses several common group communication operations used in parallel programs, including one-to-all broadcast, all-to-one reduction, all-to-all broadcast, all-reduce, and prefix-sum operations. It describes algorithms for implementing each of these operations on different network topologies like rings, meshes, and hypercubes. The algorithms are analyzed and their communication costs are derived in terms of the number of messages and message size.
In all-reduce, each node starts with a buffer of size m and the final results of the operation are identical buffers of size m on each node that are formed by combining the original p buffers using an associative operator.
This document discusses different approaches for broadcasting in hypercube networks. It describes the flooding approach which provides reliable delivery but uses excessive bandwidth. It also describes single-spanning tree broadcasting and reverse path forwarding. Single-spanning tree broadcasting restricts traffic to a single tree to avoid loops but can cause congestion. Reverse path forwarding only forwards packets along the shortest path to the source to avoid duplicates. Both approaches are suitable for hypercubes as they have inherent symmetry allowing for edge-disjoint trees and shortest paths calculated using XOR operations.
Chapter - 04 Basic Communication OperationNifras Ismail
The document discusses various communication patterns that are commonly used in parallel programs, including broadcast, reduction, scatter, and gather. Broadcast involves one process sending the same data to all other processes, while reduction involves combining data from all processes using an associative operator. These operations can be performed efficiently on networks using recursive doubling techniques. Specific algorithms are described for performing broadcast, reduction and other collectives on linear arrays, meshes, hypercubes and other network topologies.
Optimization of Collective Communication in MPICH Lino Possamai
This is a lecture about the paper: "Optimization of Collective Communication in MPICH". Department of Computer Science, University Ca' Foscari of Venice, Italy
ALGORITHMS FOR PACKET ROUTING IN SWITCHING NETWORKS WITH RECONFIGURATION OVER...csandit
Given a set of messages to be transmitted in packages from a set of sending stations to a set of
receiving stations, we are required to schedule the packages so as to achieve the minimum
possible time from the moment the 1st transmission initiates to the concluding of the last.
Preempting packets in order to reroute message remains, as part of some other packet to be
transmitted at a later time would be a great means to achieve our goal, if not for the fact that
each preemption will come with a reconfiguration cost that will delay our entire effort. The
problem has been extensively studied in the past and various algorithms have been proposed to
handle many variations of the problem. In this paper we propose an improved algorithm that we
call the Split-Graph Algorithm (SGA). To establish its efficiency we compare it, to two of the
algorithms developed in the past. These two are the best presented in bibliography so far, one in
terms of approximation ratio and one in terms of experimental results.
ENHANCEMENT OF TCP FAIRNESS IN IEEE 802.11 NETWORKScscpconf
The usage of fixed buffers in 802.11 networks has a number of disadvantages associated with
it. This includes high delay, reduced throughput and inefficient channel utilisation. To
overcome this, a dynamic buffer sizing algorithm, the A* algorithm has been implemented at
the access point. In this algorithm buffer size is dynamically adjusted depending upon the
current channel conditions and hence delay is reduced and the throughput is maintained. But
in 802.11 networks with DCF collision avoidance mechanism, it creates significant amount of
unfairness between the upstream and downstream TCP flows, with clusters of upstream ACKs
blocking downstream data at the access point. Thus a variation of the Explicit Window
Adaptation (EWA) scheme has been used to regulate the queuing time of the upload clients by
calculating the feedback value at the access point. This creates fairness and increases the number of transmission opportunities for the downstream traffic
Basic communication operations - One to all BroadcastRashiJoshi11
This document discusses one-to-all broadcast operations in parallel computing. It describes one-to-all broadcast, where a single process sends identical data to all other processes. It then discusses implementations of one-to-all broadcast on ring/linear array, mesh, and hypercube network topologies. It analyzes the time cost of one-to-all broadcast as O(logp) message transfers. It also describes how to improve the speed using a scatter-all-to-all broadcast approach for large messages.
This document discusses several common group communication operations used in parallel programs, including one-to-all broadcast, all-to-one reduction, all-to-all broadcast, all-reduce, and prefix-sum operations. It describes algorithms for implementing each of these operations on different network topologies like rings, meshes, and hypercubes. The algorithms are analyzed and their communication costs are derived in terms of the number of messages and message size.
In all-reduce, each node starts with a buffer of size m and the final results of the operation are identical buffers of size m on each node that are formed by combining the original p buffers using an associative operator.
This document discusses different approaches for broadcasting in hypercube networks. It describes the flooding approach which provides reliable delivery but uses excessive bandwidth. It also describes single-spanning tree broadcasting and reverse path forwarding. Single-spanning tree broadcasting restricts traffic to a single tree to avoid loops but can cause congestion. Reverse path forwarding only forwards packets along the shortest path to the source to avoid duplicates. Both approaches are suitable for hypercubes as they have inherent symmetry allowing for edge-disjoint trees and shortest paths calculated using XOR operations.
Chapter - 04 Basic Communication OperationNifras Ismail
The document discusses various communication patterns that are commonly used in parallel programs, including broadcast, reduction, scatter, and gather. Broadcast involves one process sending the same data to all other processes, while reduction involves combining data from all processes using an associative operator. These operations can be performed efficiently on networks using recursive doubling techniques. Specific algorithms are described for performing broadcast, reduction and other collectives on linear arrays, meshes, hypercubes and other network topologies.
Optimization of Collective Communication in MPICH Lino Possamai
This is a lecture about the paper: "Optimization of Collective Communication in MPICH". Department of Computer Science, University Ca' Foscari of Venice, Italy
ALGORITHMS FOR PACKET ROUTING IN SWITCHING NETWORKS WITH RECONFIGURATION OVER...csandit
Given a set of messages to be transmitted in packages from a set of sending stations to a set of
receiving stations, we are required to schedule the packages so as to achieve the minimum
possible time from the moment the 1st transmission initiates to the concluding of the last.
Preempting packets in order to reroute message remains, as part of some other packet to be
transmitted at a later time would be a great means to achieve our goal, if not for the fact that
each preemption will come with a reconfiguration cost that will delay our entire effort. The
problem has been extensively studied in the past and various algorithms have been proposed to
handle many variations of the problem. In this paper we propose an improved algorithm that we
call the Split-Graph Algorithm (SGA). To establish its efficiency we compare it, to two of the
algorithms developed in the past. These two are the best presented in bibliography so far, one in
terms of approximation ratio and one in terms of experimental results.
ENHANCEMENT OF TCP FAIRNESS IN IEEE 802.11 NETWORKScscpconf
The usage of fixed buffers in 802.11 networks has a number of disadvantages associated with
it. This includes high delay, reduced throughput and inefficient channel utilisation. To
overcome this, a dynamic buffer sizing algorithm, the A* algorithm has been implemented at
the access point. In this algorithm buffer size is dynamically adjusted depending upon the
current channel conditions and hence delay is reduced and the throughput is maintained. But
in 802.11 networks with DCF collision avoidance mechanism, it creates significant amount of
unfairness between the upstream and downstream TCP flows, with clusters of upstream ACKs
blocking downstream data at the access point. Thus a variation of the Explicit Window
Adaptation (EWA) scheme has been used to regulate the queuing time of the upload clients by
calculating the feedback value at the access point. This creates fairness and increases the number of transmission opportunities for the downstream traffic
AN OPEN SHOP APPROACH IN APPROXIMATING OPTIMAL DATA TRANSMISSION DURATION IN ...csandit
This document presents a hybrid algorithm (HSA) for approximating optimal data transmission duration in WDM networks. HSA reduces the preemptive bipartite scheduling problem (PBS) to open shop scheduling problems that can be solved in polynomial time. HSA combines two such algorithms, POSA and OS01PT, to minimize makespan and number of preemptions respectively. Experimental results show HSA produces schedules very close to optimal and outperforms another efficient algorithm (SGA) for PBS, with an approximation ratio up to 8% better. Future work could aim to improve HSA's time complexity or prove a better approximation ratio.
A CRITICAL IMPROVEMENT ON OPEN SHOP SCHEDULING ALGORITHM FOR ROUTING IN INTER...IJCNCJournal
In the past years, Interconnection Networks have been used quite often and especially in applications where parallelization is critical. Message packets transmitted through such networks can be interrupted
using buffers in order to maximize network usage and minimize the time required for all messages to reach
their destination. However, preempting a packet will result in topology reconfiguration and consequently in
time cost. The problem of scheduling message packets through such a network is referred to as PBS and is
known to be NP-Hard. In this paper we haveimproved,
ritically, variations of polynomially solvable
instances of Open Shop to approximate PBS. We have combined these variations and called the induced
algorithmI_HSA (Improved Hybridic Scheduling Algorithm). We ran experiments to establish the efficiency
of I_HSA and found that in all datasets used it produces schedules very close to the optimal. In addition, we
tested I_HSA with datasets that follow non-uniform distributions and provided statistical data which
illustrates better its performance.To further establish I_HSA’s efficiency we ran tests to compare it to SGA,
another algorithm which when tested in the past has yielded excellent results.
This document provides the solutions to selected problems from the textbook "Introduction to Parallel Computing". The solutions are supplemented with figures where needed. Figure and equation numbers are represented in roman numerals to differentiate them from the textbook. The document contains solutions to problems from 13 chapters of the textbook covering topics in parallel computing models, algorithms, and applications.
Fault tolerant wireless sensor mac protocol for efficient collision avoidancegraphhoc
In sensor networks communication by broadcast methods involves many hazards, especially collision. Several MAC layer protocols have been proposed to resolve the problem of collision namely ARBP, where the best achieved success rate is 90%. We hereby propose a MAC protocol which achieves a greater success rate (Success rate is defined as the percentage of delivered packets at the source reaching the destination successfully) by reducing the number of collisions, but by trading off the average propagation delay of transmission. Our proposed protocols are also shown to be more energy efficient in terms of energy dissipation per message delivery, compared to the currently existing protocol.
The document discusses technology mapping for area minimization without breaking DAGs into trees. It proposes two approaches - 1) Extending an existing algorithm called Flowmap-r by forming Maximum Fanout Free Cones (MFFCs) for the DAG and 2) A divide and conquer approach that recursively divides the problem into subproblems until reaching leaf nodes. The key steps involve generating MFFCs, finding mappable MFFCs based on a logic library, and using a weighted set cover algorithm to determine the minimum area cover.
This document discusses techniques for image coding and compression, including predicting pixel values from neighboring pixels, encoding differences between actual and predicted values (DPCM), and adapting the mapping of bits to differences over time (ADPCM). DPCM removes redundancy by transmitting only differences between samples, which are normally small. ADPCM varies this mapping dynamically so more bits can be used for rapid changes and fewer for slow changes. Overall the document focuses on prediction-based approaches to reduce image data by exploiting spatial and temporal correlations between pixels.
The document discusses analog-to-digital conversion techniques. It describes pulse code modulation (PCM) which involves sampling an analog signal, quantizing the sample amplitudes, and encoding the quantized values into binary digits. It also describes delta modulation which encodes changes in signal amplitude rather than absolute values. PCM provides higher quality reconstruction of signals but requires a higher bit rate. The Nyquist sampling theorem states the minimum required sampling rate is twice the highest frequency component of the signal.
Differential pulse-code modulation (DPCM) encodes signals by taking the difference between the current sample and a prediction of the next sample based on previous samples. This difference signal has a smaller range than the original signal and can be more efficiently quantized and encoded. DPCM uses a feedback loop where the difference is quantized, sent to the receiver, and added to the previous reconstructed sample to estimate the current sample. Adaptive delta modulation is a variant of DPCM where the quantization step size varies depending on the number of consecutive bits in the same direction to reduce errors. DPCM can reconstruct signals sampled above the Nyquist rate but may suffer from error drift or error propagation issues over multiple samples.
Ch6 1 Data communication and networking by neha g. kuraleNeha Kurale
This document discusses bandwidth utilization and multiplexing techniques. It begins by defining bandwidth utilization and how efficiency can be achieved through multiplexing, which is the set of techniques that allows simultaneous transmission of multiple signals across a single data link. The document then provides details on various multiplexing techniques including frequency-division multiplexing, wavelength-division multiplexing, synchronous time-division multiplexing, and statistical time-division multiplexing. It also discusses bandwidth matching strategies like multilevel, multislot, and pulse stuffing multiplexing and includes examples of applying these concepts.
There are three main types of multiplexing: frequency division multiplexing (FDM), time division multiplexing (TDM), and wavelength division multiplexing (WDM). FDM assigns different frequency bands to different signals, TDM divides the transmission medium into time slots and assigns each signal to a time slot, and WDM assigns different wavelength bands to different signals. Pulse code modulation (PCM) is commonly used for digital voice transmission. In PCM, the analog voice signal is sampled, quantized into digital code, and transmitted over the channel in a frame structure consisting of time slots.
Available network bandwidth schema to improve performance in tcp protocolsIJCNCJournal
The document describes a new congestion control scheme called New General Window Advertising (NGWA) for TCP. NGWA provides information on available network bandwidth to TCP endpoints. It stores the available bytes in router queues in a variable transmitted in IP headers. Receivers extract this value and use it to set the receive window size, indirectly informing senders of network capacity. Simulations show NGWA achieves stable transmission rates and fairness compared to TCP New Reno and standard TCP. An implementation in the Linux kernel proves NGWA's correct operation.
Joint Timing and Frequency Synchronization in OFDMidescitation
1) The document discusses synchronization challenges in OFDM systems, including packet detection, timing synchronization, and frequency offset calculation. It analyzes various synchronization techniques like auto-correlation difference, auto-correlation sum, and cross-correlation methods for packet detection and timing synchronization.
2) For frequency offset calculation, it describes data-aided and non-data aided algorithms, including the van De Beek algorithm which relies on cyclic prefix redundancy rather than pilot symbols.
3) The key synchronization challenges are maintaining orthogonality between subcarriers in the presence of frequency offsets introduced by the wireless channel, which can significantly degrade performance if not corrected. Accurate synchronization algorithms are important for OFDM receivers to function properly.
These slides cover a topic on Wave Division Multiplexing in Data Communication. All the slides are explained in a very simple manner. It is useful for engineering students & also for the candidates who want to master data communication & computer networking.
This document discusses multiplexing techniques for sharing bandwidth between multiple users. It describes how multiplexing allows simultaneous transmission of multiple signals across a single data link. The key multiplexing techniques covered are frequency-division multiplexing (FDM), wavelength-division multiplexing (WDM), time-division multiplexing (TDM), and statistical time-division multiplexing. Examples are provided to illustrate concepts like FDM configuration, guard bands, bandwidth calculation, data rate matching through multilevel, multislot and pulse stuffing techniques, and frame synchronization.
This document discusses multiplexing techniques for bandwidth utilization including frequency-division multiplexing (FDM), wavelength-division multiplexing (WDM), time-division multiplexing (TDM), and statistical time-division multiplexing. It provides examples of combining multiple analog or digital signals into a single transmission medium and discusses frame rates, bit rates, and slot durations. Synchronization and data rate management techniques are also covered to efficiently allocate bandwidth when input link speeds are mismatched.
Ch3 3 Data communication and networking Neha Kurale
This document discusses key networking performance terms such as bandwidth, throughput, latency, and bandwidth-delay product. It defines bandwidth as the capacity of a system to transmit data, measured in bits per second. Throughput is the actual number of bits transmitted through a network. Latency refers to the delay for a bit to travel from source to destination. Bandwidth-delay product represents the number of bits that can fill the transmission link between two points, which is important for efficient network operation. Examples are provided to illustrate how to calculate propagation delay, transmission delay, and bandwidth-delay product in different scenarios.
This document discusses multiplexing and spreading techniques for bandwidth utilization and privacy/anti-jamming. It covers frequency division multiplexing (FDM), wavelength division multiplexing (WDM), time division multiplexing (TDM), statistical TDM, inverse multiplexing, frequency hopping spread spectrum (FHSS), and direct sequence spread spectrum (DSSS). Examples are provided for combining voice channels using FDM, optical signal multiplexing with WDM, and modulating data streams for transmission using TDM, FHSS, and DSSS. Common applications discussed include radio/TV broadcasting, fiber optic networks, telephone systems, and digital subscriber lines.
A comparison of efficient algorithms for scheduling parallel data redistributionIJCNCJournal
This document compares algorithms for scheduling parallel data redistribution. It proposes a new algorithm called the Split Graph Algorithm (SGA) that splits the data into two clusters based on size and schedules large and small data differently. SGA was tested on 1000 test cases and found to produce schedules closer to the theoretical lower bound and faster than two existing algorithms, demonstrating its efficiency.
This document summarizes basic communication operations for parallel computing including:
- One-to-all broadcast and all-to-one reduction which involve sending a message from one processor to all others or combining messages from all processors to one.
- All-to-all broadcast and reduction where all processors simultaneously broadcast or reduce messages.
- Collective operations like all-reduce and prefix-sum which combine messages from all processors using associative operators.
- Examples of implementing these operations on different network topologies like rings, meshes and hypercubes are presented along with analyzing their communication costs. The document provides an overview of fundamental communication patterns in parallel computing.
This document summarizes several algorithms for parallel matrix operations, including matrix-vector multiplication, matrix-matrix multiplication, and solving systems of linear equations via Gaussian elimination. For matrix-vector multiplication, it describes row-wise and column-wise partitioning approaches. For matrix-matrix multiplication, it discusses algorithms based on row/column broadcasting, Cannon's algorithm, and a 3D domain decomposition approach. For Gaussian elimination, it analyzes pipelined and 2D mapping implementations. The key aspects of parallelization, communication costs, computation loads, scalability, and cost efficiency are analyzed for each algorithm.
This document summarizes several dense matrix algorithms for operations like matrix-vector multiplication, matrix-matrix multiplication, and solving systems of linear equations.
For matrix-vector multiplication, it describes 1D and 2D row-wise partitioning approaches. The 2D approach has lower parallel runtime of O(log n) but requires n2 processes. A modified 2D approach uses block partitioning and has parallel runtime of O(n/√p + log p) when using p < n2 processes.
For matrix-matrix multiplication, simple parallel and Canon's algorithms are described. Canon's algorithm has optimal O(n3) memory usage by rotating matrix blocks among processes. A DNS algorithm achieves optimal O(log n
The document discusses communication costs in parallel machines. It summarizes models for estimating the time required to transfer messages between nodes in different network topologies. The models account for startup time, per-hop transfer time, and per-word transfer time. Cut-through routing aims to minimize overhead by ensuring all message parts follow the same path. The document also covers techniques for mapping different graph structures like meshes and hypercubes onto each other to facilitate communication in various parallel architectures.
AN OPEN SHOP APPROACH IN APPROXIMATING OPTIMAL DATA TRANSMISSION DURATION IN ...csandit
This document presents a hybrid algorithm (HSA) for approximating optimal data transmission duration in WDM networks. HSA reduces the preemptive bipartite scheduling problem (PBS) to open shop scheduling problems that can be solved in polynomial time. HSA combines two such algorithms, POSA and OS01PT, to minimize makespan and number of preemptions respectively. Experimental results show HSA produces schedules very close to optimal and outperforms another efficient algorithm (SGA) for PBS, with an approximation ratio up to 8% better. Future work could aim to improve HSA's time complexity or prove a better approximation ratio.
A CRITICAL IMPROVEMENT ON OPEN SHOP SCHEDULING ALGORITHM FOR ROUTING IN INTER...IJCNCJournal
In the past years, Interconnection Networks have been used quite often and especially in applications where parallelization is critical. Message packets transmitted through such networks can be interrupted
using buffers in order to maximize network usage and minimize the time required for all messages to reach
their destination. However, preempting a packet will result in topology reconfiguration and consequently in
time cost. The problem of scheduling message packets through such a network is referred to as PBS and is
known to be NP-Hard. In this paper we haveimproved,
ritically, variations of polynomially solvable
instances of Open Shop to approximate PBS. We have combined these variations and called the induced
algorithmI_HSA (Improved Hybridic Scheduling Algorithm). We ran experiments to establish the efficiency
of I_HSA and found that in all datasets used it produces schedules very close to the optimal. In addition, we
tested I_HSA with datasets that follow non-uniform distributions and provided statistical data which
illustrates better its performance.To further establish I_HSA’s efficiency we ran tests to compare it to SGA,
another algorithm which when tested in the past has yielded excellent results.
This document provides the solutions to selected problems from the textbook "Introduction to Parallel Computing". The solutions are supplemented with figures where needed. Figure and equation numbers are represented in roman numerals to differentiate them from the textbook. The document contains solutions to problems from 13 chapters of the textbook covering topics in parallel computing models, algorithms, and applications.
Fault tolerant wireless sensor mac protocol for efficient collision avoidancegraphhoc
In sensor networks communication by broadcast methods involves many hazards, especially collision. Several MAC layer protocols have been proposed to resolve the problem of collision namely ARBP, where the best achieved success rate is 90%. We hereby propose a MAC protocol which achieves a greater success rate (Success rate is defined as the percentage of delivered packets at the source reaching the destination successfully) by reducing the number of collisions, but by trading off the average propagation delay of transmission. Our proposed protocols are also shown to be more energy efficient in terms of energy dissipation per message delivery, compared to the currently existing protocol.
The document discusses technology mapping for area minimization without breaking DAGs into trees. It proposes two approaches - 1) Extending an existing algorithm called Flowmap-r by forming Maximum Fanout Free Cones (MFFCs) for the DAG and 2) A divide and conquer approach that recursively divides the problem into subproblems until reaching leaf nodes. The key steps involve generating MFFCs, finding mappable MFFCs based on a logic library, and using a weighted set cover algorithm to determine the minimum area cover.
This document discusses techniques for image coding and compression, including predicting pixel values from neighboring pixels, encoding differences between actual and predicted values (DPCM), and adapting the mapping of bits to differences over time (ADPCM). DPCM removes redundancy by transmitting only differences between samples, which are normally small. ADPCM varies this mapping dynamically so more bits can be used for rapid changes and fewer for slow changes. Overall the document focuses on prediction-based approaches to reduce image data by exploiting spatial and temporal correlations between pixels.
The document discusses analog-to-digital conversion techniques. It describes pulse code modulation (PCM) which involves sampling an analog signal, quantizing the sample amplitudes, and encoding the quantized values into binary digits. It also describes delta modulation which encodes changes in signal amplitude rather than absolute values. PCM provides higher quality reconstruction of signals but requires a higher bit rate. The Nyquist sampling theorem states the minimum required sampling rate is twice the highest frequency component of the signal.
Differential pulse-code modulation (DPCM) encodes signals by taking the difference between the current sample and a prediction of the next sample based on previous samples. This difference signal has a smaller range than the original signal and can be more efficiently quantized and encoded. DPCM uses a feedback loop where the difference is quantized, sent to the receiver, and added to the previous reconstructed sample to estimate the current sample. Adaptive delta modulation is a variant of DPCM where the quantization step size varies depending on the number of consecutive bits in the same direction to reduce errors. DPCM can reconstruct signals sampled above the Nyquist rate but may suffer from error drift or error propagation issues over multiple samples.
Ch6 1 Data communication and networking by neha g. kuraleNeha Kurale
This document discusses bandwidth utilization and multiplexing techniques. It begins by defining bandwidth utilization and how efficiency can be achieved through multiplexing, which is the set of techniques that allows simultaneous transmission of multiple signals across a single data link. The document then provides details on various multiplexing techniques including frequency-division multiplexing, wavelength-division multiplexing, synchronous time-division multiplexing, and statistical time-division multiplexing. It also discusses bandwidth matching strategies like multilevel, multislot, and pulse stuffing multiplexing and includes examples of applying these concepts.
There are three main types of multiplexing: frequency division multiplexing (FDM), time division multiplexing (TDM), and wavelength division multiplexing (WDM). FDM assigns different frequency bands to different signals, TDM divides the transmission medium into time slots and assigns each signal to a time slot, and WDM assigns different wavelength bands to different signals. Pulse code modulation (PCM) is commonly used for digital voice transmission. In PCM, the analog voice signal is sampled, quantized into digital code, and transmitted over the channel in a frame structure consisting of time slots.
Available network bandwidth schema to improve performance in tcp protocolsIJCNCJournal
The document describes a new congestion control scheme called New General Window Advertising (NGWA) for TCP. NGWA provides information on available network bandwidth to TCP endpoints. It stores the available bytes in router queues in a variable transmitted in IP headers. Receivers extract this value and use it to set the receive window size, indirectly informing senders of network capacity. Simulations show NGWA achieves stable transmission rates and fairness compared to TCP New Reno and standard TCP. An implementation in the Linux kernel proves NGWA's correct operation.
Joint Timing and Frequency Synchronization in OFDMidescitation
1) The document discusses synchronization challenges in OFDM systems, including packet detection, timing synchronization, and frequency offset calculation. It analyzes various synchronization techniques like auto-correlation difference, auto-correlation sum, and cross-correlation methods for packet detection and timing synchronization.
2) For frequency offset calculation, it describes data-aided and non-data aided algorithms, including the van De Beek algorithm which relies on cyclic prefix redundancy rather than pilot symbols.
3) The key synchronization challenges are maintaining orthogonality between subcarriers in the presence of frequency offsets introduced by the wireless channel, which can significantly degrade performance if not corrected. Accurate synchronization algorithms are important for OFDM receivers to function properly.
These slides cover a topic on Wave Division Multiplexing in Data Communication. All the slides are explained in a very simple manner. It is useful for engineering students & also for the candidates who want to master data communication & computer networking.
This document discusses multiplexing techniques for sharing bandwidth between multiple users. It describes how multiplexing allows simultaneous transmission of multiple signals across a single data link. The key multiplexing techniques covered are frequency-division multiplexing (FDM), wavelength-division multiplexing (WDM), time-division multiplexing (TDM), and statistical time-division multiplexing. Examples are provided to illustrate concepts like FDM configuration, guard bands, bandwidth calculation, data rate matching through multilevel, multislot and pulse stuffing techniques, and frame synchronization.
This document discusses multiplexing techniques for bandwidth utilization including frequency-division multiplexing (FDM), wavelength-division multiplexing (WDM), time-division multiplexing (TDM), and statistical time-division multiplexing. It provides examples of combining multiple analog or digital signals into a single transmission medium and discusses frame rates, bit rates, and slot durations. Synchronization and data rate management techniques are also covered to efficiently allocate bandwidth when input link speeds are mismatched.
Ch3 3 Data communication and networking Neha Kurale
This document discusses key networking performance terms such as bandwidth, throughput, latency, and bandwidth-delay product. It defines bandwidth as the capacity of a system to transmit data, measured in bits per second. Throughput is the actual number of bits transmitted through a network. Latency refers to the delay for a bit to travel from source to destination. Bandwidth-delay product represents the number of bits that can fill the transmission link between two points, which is important for efficient network operation. Examples are provided to illustrate how to calculate propagation delay, transmission delay, and bandwidth-delay product in different scenarios.
This document discusses multiplexing and spreading techniques for bandwidth utilization and privacy/anti-jamming. It covers frequency division multiplexing (FDM), wavelength division multiplexing (WDM), time division multiplexing (TDM), statistical TDM, inverse multiplexing, frequency hopping spread spectrum (FHSS), and direct sequence spread spectrum (DSSS). Examples are provided for combining voice channels using FDM, optical signal multiplexing with WDM, and modulating data streams for transmission using TDM, FHSS, and DSSS. Common applications discussed include radio/TV broadcasting, fiber optic networks, telephone systems, and digital subscriber lines.
A comparison of efficient algorithms for scheduling parallel data redistributionIJCNCJournal
This document compares algorithms for scheduling parallel data redistribution. It proposes a new algorithm called the Split Graph Algorithm (SGA) that splits the data into two clusters based on size and schedules large and small data differently. SGA was tested on 1000 test cases and found to produce schedules closer to the theoretical lower bound and faster than two existing algorithms, demonstrating its efficiency.
This document summarizes basic communication operations for parallel computing including:
- One-to-all broadcast and all-to-one reduction which involve sending a message from one processor to all others or combining messages from all processors to one.
- All-to-all broadcast and reduction where all processors simultaneously broadcast or reduce messages.
- Collective operations like all-reduce and prefix-sum which combine messages from all processors using associative operators.
- Examples of implementing these operations on different network topologies like rings, meshes and hypercubes are presented along with analyzing their communication costs. The document provides an overview of fundamental communication patterns in parallel computing.
This document summarizes several algorithms for parallel matrix operations, including matrix-vector multiplication, matrix-matrix multiplication, and solving systems of linear equations via Gaussian elimination. For matrix-vector multiplication, it describes row-wise and column-wise partitioning approaches. For matrix-matrix multiplication, it discusses algorithms based on row/column broadcasting, Cannon's algorithm, and a 3D domain decomposition approach. For Gaussian elimination, it analyzes pipelined and 2D mapping implementations. The key aspects of parallelization, communication costs, computation loads, scalability, and cost efficiency are analyzed for each algorithm.
This document summarizes several dense matrix algorithms for operations like matrix-vector multiplication, matrix-matrix multiplication, and solving systems of linear equations.
For matrix-vector multiplication, it describes 1D and 2D row-wise partitioning approaches. The 2D approach has lower parallel runtime of O(log n) but requires n2 processes. A modified 2D approach uses block partitioning and has parallel runtime of O(n/√p + log p) when using p < n2 processes.
For matrix-matrix multiplication, simple parallel and Canon's algorithms are described. Canon's algorithm has optimal O(n3) memory usage by rotating matrix blocks among processes. A DNS algorithm achieves optimal O(log n
The document discusses communication costs in parallel machines. It summarizes models for estimating the time required to transfer messages between nodes in different network topologies. The models account for startup time, per-hop transfer time, and per-word transfer time. Cut-through routing aims to minimize overhead by ensuring all message parts follow the same path. The document also covers techniques for mapping different graph structures like meshes and hypercubes onto each other to facilitate communication in various parallel architectures.
This document discusses various types of interconnect networks that can be used to connect processors and memory in parallel computers. It describes dynamic interconnects like crossbar switches and bus-based networks that are commonly used for shared memory systems. It also describes static interconnects like completely connected, star connected, linear arrays, rings, meshes, torus and hypercubes typically used for message passing systems. It provides details on different properties of these networks like diameter, connectivity, bisection width etc. It also discusses performance modeling and sources of overhead in parallel systems.
This document discusses various communication patterns in parallel and distributed systems including one-to-all broadcast, all-to-one reduction, all-to-all broadcast and reduction, all-reduce, prefix-sum, scatter, gather, and circular shift operations. It describes how to perform these operations efficiently using techniques like recursive doubling and message splitting. Improving the performance of common communication operations can be done by splitting large messages into smaller parts and combining different patterns like scatter, all-to-all, and gather.
The document provides an overview of backpropagation, a common algorithm used to train multi-layer neural networks. It discusses:
- How backpropagation works by calculating error terms for output nodes and propagating these errors back through the network to adjust weights.
- The stages of feedforward activation and backpropagation of errors to update weights.
- Options like initial random weights, number of training cycles and hidden nodes.
- An example of using backpropagation to train a network to learn the XOR function over multiple training passes of forward passing and backward error propagation and weight updating.
This document discusses loop parallelization and pipelining as well as trends in parallel systems and forms of parallelism. It describes loop transformations like permutation, reversal, and skewing that can be used to parallelize loops. It also discusses parallelization conditions, wavefront transformations for fine-grained parallelism, and tiling to improve data locality. The document then covers software pipelining of loops to reduce execution time. Finally, it discusses trends in parallel computing and different forms of parallelism like instruction-level, data, and task parallelism.
MANET Routing Protocols , a case studyRehan Hattab
L. Yi, Y. Zhai, Y. Wang, J. Yuan and I. You , Impacts of Internal Network Contexts on Performance of MANET Routing Protocols: a Case Study, Sixth International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing,2012.
The document discusses parallel algorithms and parallel computing. It begins by defining parallelism in computers as performing more than one task at the same time. Examples of parallelism include I/O chips and pipelining of instructions. Common terms for parallelism are defined, including concurrent processing, distributed processing, and parallel processing. Issues in parallel programming such as task decomposition and synchronization are outlined. Performance issues like scalability and load balancing are also discussed. Different types of parallel machines and their classification are described.
SLM-PTS BASED PAPR REDUCTION TECHNIQUES IN OFDM SYSTEMHariniChaganti1
Signals, which were initially sent in the analog domain, are being sent more and more in the digital domain these days. For better transmission, even single–carrier waves are being replaced by multi–carriers. Multi-carrier
systems like OFDM are now – a – days being implemented commonly. In the OFDM system,
orthogonally placed subcarriers are used to carry the data from the transmitter end to the receiver end. The presence of a guard band in this system deals with the problem of ISI and noise is minimized by a larger number of sub–carriers. But the large Peak– to –Average Power Ratio of these signal have some undesirable effects on the system. The Peak-to-Average Power Ratio is the ratio between the maximum power and average power of a complex passband signal. It causes many disadvantages like band-in and band-out variation, low signal to quantization noise ratio, low efficiency of power amplifier, etc. Hence, it is necessary to reduce PAPR in OFDM for its efficient use.
In this project, the main objective is to study the basics of an OFDM System and analyze and
simulate various methods such as clipping and filtering, selected mapping, Partial transmit sequence
to reduce the PAPR in the system and compare these techniques with and without PAPR reduction to
obtain an efficient technique so that this system can be used more commonly and effectively.
This document describes a parallel algorithm for batched range searching on coarse-grained multicomputers. The algorithm is based on the range-tree method and solves the d-dimensional batched range searching problem in O(Ts(nlogd-1p;p)+Ts(mlogd-1p;p)+((m+n)logd-1(n/p)+mlogd-1plog(n/p)+k)/p) time. It constructs a range tree in parallel by sorting points and building subtrees on each processor. It then partitions query ranges and determines contained points in parallel by traversing the range tree.
An Open Shop Approach in Approximating Optimal Data Transmission Duration in ...cscpconf
In the past decade Optical WDM Networks (Wavelength Division Multiplexing) are being used
quite often and especially as far as broadband applications are concerned. Message packets
transmitted through such networks can be interrupted using time slots in order to maximize
network usage and minimize the time required for all messages to reach their destination.
However, preempting a packet will result in time cost. The problem of scheduling message
packets through such a network is referred to as PBS and is known to be NP-Hard. In this paper
we have reduced PBS to Open Shop Scheduling and designed variations of polynomially
solvable instances of Open Shop to approximate PBS. We have combined these variations and
called the induced algorithm HSA (Hybridic Scheduling Algorithm). We ran experiments to
establish the efficiency of HSA and found that in all datasets used it produces schedules very
close to the optimal. To further establish HSA’s efficiency we ran tests to compare it to SGA,
another algorithm which when tested in the past has yielded excellent results.
Synchronization of multihop sensor networks in the app layerVaishnavi
The document describes a synchronization protocol called Multihop Broadcast Synchronization (MBS) for wireless sensor networks. MBS achieves synchronization across multiple hops in the network through the exchange of two message types between propagator and timestamper nodes. Propagator nodes broadcast synchronization messages containing timestamps, while timestamper nodes respond with the timestamps of received messages. By collecting multiple timestamp pairs, nodes can synchronize their clocks to the global network time with minimal message overhead.
This document discusses analytical modeling of parallel systems. It begins by outlining topics like sources of overhead in parallel programs, performance metrics, and scalability. It then discusses basics of analytical modeling, noting that parallel runtime depends on input size, number of processors, and machine communication parameters. Several performance measures are introduced, like wall clock time and speedup. Sources of overhead like idling, excess computation, and communication are described. Metrics like parallel time, total overhead, speedup, and efficiency are formally defined. The impact of non-cost optimality and ways to build granularity are discussed. Finally, scaling characteristics and isoefficiency as a metric of scalability are covered.
A natural extension of the Random Access Machine (RAM) serial architecture is the Parallel Random Access Machine, or PRAM.
PRAMs consist of p processors and a global memory of unbounded size that is uniformly accessible to all processors.
Processors share a common clock but may execute different instructions in each cycle.
Here is a Python program to train and simulate a neural network with 2 input nodes, 1 hidden layer with 3 nodes, and 1 output node to perform an XOR operation:
```python
import numpy as np
# Network parameters
num_input = 2 # Input nodes
num_hidden = 3 # Hidden layer nodes
num_output = 1 # Output node
# Training data
X = np.array([[0,0], [0,1], [1,0], [1,1]])
y = np.array([[0], [1], [1], [0]])
# Initialize weights randomly with mean 0
hidden_weights = 2*np.random.random((num_
Slides reviewing the paper:
Vaswani, Ashish, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, and Illia Polosukhin. "Attention is all you need." In Advances in Neural Information Processing Systems, pp. 6000-6010. 2017.
The dominant sequence transduction models are based on complex recurrent orconvolutional neural networks in an encoder and decoder configuration. The best performing such models also connect the encoder and decoder through an attentionm echanisms. We propose a novel, simple network architecture based solely onan attention mechanism, dispensing with recurrence and convolutions entirely.Experiments on two machine translation tasks show these models to be superiorin quality while being more parallelizable and requiring significantly less timeto train. Our single model with 165 million parameters, achieves 27.5 BLEU onEnglish-to-German translation, improving over the existing best ensemble result by over 1 BLEU. On English-to-French translation, we outperform the previoussingle state-of-the-art with model by 0.7 BLEU, achieving a BLEU score of 41.1.
The document discusses parallel algorithms and their analysis. It introduces a simple parallel algorithm for adding n numbers using log n steps. Parallel algorithms are analyzed based on their time complexity, processor complexity, and work complexity. For adding n numbers in parallel, the time complexity is O(log n), processor complexity is O(n), and work complexity is O(n log n). The document also discusses models of parallel computation like PRAM and designs of parallel architectures like meshes and hypercubes.
SIET Kerala is responsible for planning, researching, producing, and evaluating educational software, videos, audio programs, and computer multimedia in Kerala, India. It aims to modernize teaching technologies and learning processes. The Institute plays a catalytic role in supporting and supplementing education, particularly secondary and higher secondary education. It produces video and audio programs for students ages 5 to 17 and teachers in regional languages to supplement classroom teaching. Some of its programs include educational TV, film festivals, and a CD library project. The educational programs produced by SIET have received wide acclaim from students, teachers, and parents in Kerala.
This document outlines a lesson plan about work, power, and energy. The lesson includes motivating students with questions, guided reading of the text, forming mind maps in groups, and consolidation of key facts such as the definitions of work, force, and displacement. Students then present their mind maps and compare them to the teacher's version. Formative assessment includes multiple choice questions to check understanding.
Electricity plays an important role in modern life and is obtained through power stations and batteries. Electric current flows through closed circuits that are made up of a power source connected to devices like bulbs through switches and wires. There are three main types of circuits: simple circuits with one bulb, series circuits where the bulbs are connected end to end and the same current flows through each, and parallel circuits where each bulb has a separate path and different currents can flow through each.
This document defines attitudes and discusses several theories related to how attitudes form and change. It provides the following key points in 3 sentences:
Attitudes are psychological tendencies to evaluate entities favorably or unfavorably and are composed of affective, behavioral, and cognitive components. Several theories discussed how attitudes are influenced by cognitive dissonance when behavior contradicts attitudes, and self-perception theory suggests attitudes can form from inferring them based on own behavior. The theory of planned behavior models how behavioral intentions are influenced by attitudes, subjective norms, and perceived behavioral control.
Dmitri Mendeleev was a Russian chemist born in 1834. He studied chemistry and graduated from St. Petersburg University in 1856. After graduating, he became a professor and was considered one of the greatest chemistry teachers of his time. Mendeleev is most famous for creating the first version of the periodic table of elements in 1869, in which he arranged the elements based on their atomic weights and properties. Using his periodic table, he was able to predict the properties of elements that had not yet been discovered. The periodic table became widely accepted among chemists and helped advance the field of chemistry. Mendeleev received several honors for his work, including the Copley Medal, and element 101 was named Mende
SIET Kerala is responsible for planning, researching, producing, and evaluating educational software, videos, audio programs, and computer multimedia for students aged 5 to 17 in Kerala, India. It aims to develop modern teaching technologies and learning processes. SIET Kerala produces educational TV and film programs that have received wide acclaim from students, teachers, and parents. It broadcasts programs daily on television and through the EDUSAT education channel. SIET has also produced over 900 educational CDs in English and Malayalam and implemented a CD library project in over 9,000 schools across Kerala.
SIET Kerala is responsible for planning, producing, and evaluating educational software, videos, audio programs, and multimedia for schools in Kerala. It aims to develop modern teaching technologies and improve the learning process. The Institute supports and supplements educational development in secondary and higher secondary education by preparing video and audio programs in local languages to complement classroom teaching for students ages 5 to 17. It produces educational television programs, film festivals, and has produced over 900 educational CDs in English and Malayalam that have been distributed to schools through its CD Library Project.
Dmitri Mendeleev was a Russian chemist born in 1834. He studied chemistry and became a professor. He is most famous for creating the first periodic table of elements in 1869, arranging elements based on atomic weight and properties. His periodic table predicted properties of undiscovered elements and helped establish the modern organization of elements that is still used today.
Dmitri Mendeleev was a Russian chemist born in 1834. He studied chemistry and became a professor. He is most famous for creating the first periodic table of elements in 1869, arranging elements by atomic weight and properties. His periodic table allowed him to predict properties of undiscovered elements and is the foundation for how the elements are organized today. Mendeleev made many contributions to chemistry and was honored with awards from the Royal Society of England.
This document discusses creativity and the need for a science-based definition and approach to teaching it in schools. It defines creativity as the ability to bring something new into existence from future possibilities, generated from our inner domain of being. The document explains how our perception of reality has changed from a Newtonian space-time view to Einstein's space/time view. It presents creativity as a basic operating system for human actions and problem solving. It argues that developing the domain of knowing with more knowledge must be paired with using the domain of being and creativity. A basic course in creativity could provide a breakthrough in education by facilitating learning across other subjects.
This document discusses various group communication operations that are commonly used in parallel programs. It begins with an introduction and overview of operations like one-to-all broadcast, all-to-one reduction, all-to-all broadcast, all-reduce, scatter, gather, and all-to-all personalized communication. It then provides detailed descriptions and algorithms for how to implement each of these operations on different network topologies like rings, meshes, hypercubes, and trees. It analyzes the time complexity of each algorithm and compares different approaches. The goal is to provide efficient implementations of these fundamental communication patterns.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
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.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
2. Topic Overview
• One-to-All Broadcast and All-to-One Reduction
• All-to-All Broadcast and Reduction
• All-Reduce and Prefix-Sum Operations
• Scatter and Gather
• All-to-All Personalized Communication
• Circular Shift
• Improving the Speed of Some Communication
Operations
3. Basic Communication Operations:
Introduction
• Many interactions in practical parallel programs occur in
well-defined patterns involving groups of processors.
• Efficient implementations of these operations can
improve performance, reduce development effort and
cost, and improve software quality.
• Efficient implementations must leverage underlying
architecture. For this reason, we refer to specific
architectures here.
• We select a descriptive set of architectures to illustrate
the process of algorithm design.
4. Basic Communication Operations:
Introduction
• Group communication operations are built using point-to-
point messaging primitives.
• Recall from our discussion of architectures that
communicating a message of size m over an
uncongested network takes time ts +tmw.
• We use this as the basis for our analyses. Where
necessary, we take congestion into account explicitly by
scaling the tw term.
• We assume that the network is bidirectional and that
communication is single-ported.
5. One-to-All Broadcast and All-to-One
Reduction
• One processor has a piece of data (of size m) it needs to
send to everyone.
• The dual of one-to-all broadcast is all-to-one reduction.
• In all-to-one reduction, each processor has m units of
data. These data items must be combined piece-wise
(using some associative operator, such as addition or
min), and the result made available at a target
processor.
6. One-to-All Broadcast and All-to-One
Reduction
One-to-all broadcast and all-to-one reduction among processors.
7. One-to-All Broadcast and All-to-One
Reduction on Rings
• Simplest way is to send p-1 messages from the source
to the other p-1 processors - this is not very efficient.
• Use recursive doubling: source sends a message to a
selected processor. We now have two independent
problems derined over halves of machines.
• Reduction can be performed in an identical fashion by
inverting the process.
8. One-to-All Broadcast
One-to-all broadcast on an eight-node ring. Node 0 is the source of the
broadcast. Each message transfer step is shown by a numbered,
dotted arrow from the source of the message to its destination. The
number on an arrow indicates the time step during which the
message is transferred.
10. Broadcast and Reduction: Example
Consider the problem of multiplying a matrix with a vector.
• The n x n matrix is assigned to an n x n (virtual) processor grid. The
vector is assumed to be on the first row of processors.
• The first step of the product requires a one-to-all broadcast of the
vector element along the corresponding column of processors. This
can be done concurrently for all n columns.
• The processors compute local product of the vector element and the
local matrix entry.
• In the final step, the results of these products are accumulated to
the first row using n concurrent all-to-one reduction operations along
the columns (using the sum operation).
11. Broadcast and Reduction: Matrix-Vector
Multiplication Example
One-to-all broadcast and all-to-one reduction in the multiplication of a 4
x 4 matrix with a 4 x 1 vector.
12. Broadcast and Reduction on a Mesh
• We can view each row and column of a square mesh of
p nodes as a linear array of √p nodes.
• Broadcast and reduction operations can be performed in
two steps - the first step does the operation along a row
and the second step along each column concurrently.
• This process generalizes to higher dimensions as well.
14. Broadcast and Reduction on a
Hypercube
• A hypercube with 2d
nodes can be regarded as a d-
dimensional mesh with two nodes in each dimension.
• The mesh algorithm can be generalized to a hypercube
and the operation is carried out in d (= log p) steps.
15. Broadcast and Reduction on a
Hypercube: Example
One-to-all broadcast on a three-dimensional hypercube.
The binary representations of node labels are shown in
parentheses.
16. Broadcast and Reduction on a Balanced
Binary Tree
• Consider a binary tree in which processors are (logically)
at the leaves and internal nodes are routing nodes.
• Assume that source processor is the root of this tree. In
the first step, the source sends the data to the right child
(assuming the source is also the left child). The problem
has now been decomposed into two problems with half
the number of processors.
17. Broadcast and Reduction on a Balanced
Binary Tree
One-to-all broadcast on an eight-node tree.
18. Broadcast and Reduction Algorithms
• All of the algorithms described above are adaptations of
the same algorithmic template.
• We illustrate the algorithm for a hypercube, but the
algorithm, as has been seen, can be adapted to other
architectures.
• The hypercube has 2d
nodes and my_id is the label for a
node.
• X is the message to be broadcast, which initially resides
at the source node 0.
19. Broadcast and Reduction Algorithms
One-to-all broadcast of a message X from source on a hypercube.
20. Broadcast and Reduction Algorithms
Single-node accumulation on a d-dimensional hypercube. Each node contributes a message X containing m words,
and node 0 is the destination.
21. Cost Analysis
• The broadcast or reduction procedure involves log p
point-to-point simple message transfers, each at a time
cost of ts + twm.
• The total time is therefore given by:
22. All-to-All Broadcast and Reduction
• Generalization of broadcast in which each processor is
the source as well as destination.
• A process sends the same m-word message to every
other process, but different processes may broadcast
different messages.
24. All-to-All Broadcast and Reduction on a
Ring
• Simplest approach: perform p one-to-all broadcasts. This
is not the most efficient way, though.
• Each node first sends to one of its neighbors the data it
needs to broadcast.
• In subsequent steps, it forwards the data received from
one of its neighbors to its other neighbor.
• The algorithm terminates in p-1 steps.
27. All-to-all Broadcast on a Mesh
• Performed in two phases - in the first phase, each row of
the mesh performs an all-to-all broadcast using the
procedure for the linear array.
• In this phase, all nodes collect √p messages
corresponding to the √p nodes of their respective rows.
Each node consolidates this information into a single
message of size m√p.
• The second communication phase is a columnwise all-
to-all broadcast of the consolidated messages.
28. All-to-all Broadcast on a Mesh
All-to-all broadcast on a 3 x 3 mesh. The groups of nodes
communicating with each other in each phase are enclosed by
dotted boundaries. By the end of the second phase, all nodes get
(0,1,2,3,4,5,6,7) (that is, a message from each node).
33. All-to-all Reduction
• Similar communication pattern to all-to-all broadcast,
except in the reverse order.
• On receiving a message, a node must combine it with
the local copy of the message that has the same
destination as the received message before forwarding
the combined message to the next neighbor.
34. Cost Analysis
• On a ring, the time is given by: (ts + twm)(p-1).
• On a mesh, the time is given by: 2ts(√p – 1) + twm(p-1).
• On a hypercube, we have:
35. All-to-all broadcast: Notes
• All of the algorithms presented above are asymptotically
optimal in message size.
• It is not possible to port algorithms for higher
dimensional networks (such as a hypercube) into a ring
because this would cause contention.
37. All-Reduce and Prefix-Sum Operations
• In all-reduce, each node starts with a buffer of size m
and the final results of the operation are identical buffers
of size m on each node that are formed by combining the
original p buffers using an associative operator.
• Identical to all-to-one reduction followed by a one-to-all
broadcast. This formulation is not the most efficient.
Uses the pattern of all-to-all broadcast, instead. The only
difference is that message size does not increase here.
Time for this operation is (ts + twm) log p.
• Different from all-to-all reduction, in which p
simultaneous all-to-one reductions take place, each with
a different destination for the result.
38. The Prefix-Sum Operation
• Given p numbers n0,n1,…,np-1 (one on each node), the
problem is to compute the sums sk = ∑i
k
= 0 ni for all k
between 0 and p-1 .
• Initially, nk resides on the node labeled k, and at the end
of the procedure, the same node holds Sk.
39. The Prefix-Sum Operation
Computing prefix sums on an eight-node hypercube. At each node, square
brackets show the local prefix sum accumulated in the result buffer and
parentheses enclose the contents of the outgoing message buffer for the
next step.
40. The Prefix-Sum Operation
• The operation can be implemented using the all-to-all
broadcast kernel.
• We must account for the fact that in prefix sums the
node with label k uses information from only the k-node
subset whose labels are less than or equal to k.
• This is implemented using an additional result buffer.
The content of an incoming message is added to the
result buffer only if the message comes from a node with
a smaller label than the recipient node.
• The contents of the outgoing message (denoted by
parentheses in the figure) are updated with every
incoming message.
42. Scatter and Gather
• In the scatter operation, a single node sends a unique
message of size m to every other node (also called a
one-to-all personalized communication).
• In the gather operation, a single node collects a unique
message from each node.
• While the scatter operation is fundamentally different
from broadcast, the algorithmic structure is similar,
except for differences in message sizes (messages get
smaller in scatter and stay constant in broadcast).
• The gather operation is exactly the inverse of the scatter
operation and can be executed as such.
44. Example of the Scatter Operation
The scatter operation on an eight-node hypercube.
45. Cost of Scatter and Gather
• There are log p steps, in each step, the machine size
halves and the data size halves.
• We have the time for this operation to be:
• This time holds for a linear array as well as a 2-D mesh.
• These times are asymptotically optimal in message size.
46. All-to-All Personalized Communication
• Each node has a distinct message of size m for every
other node.
• This is unlike all-to-all broadcast, in which each node
sends the same message to all other nodes.
• All-to-all personalized communication is also known as
total exchange.
48. All-to-All Personalized Communication:
Example
• Consider the problem of transposing a matrix.
• Each processor contains one full row of the matrix.
• The transpose operation in this case is identical to an all-
to-all personalized communication operation.
50. All-to-All Personalized Communication
on a Ring
• Each node sends all pieces of data as one consolidated
message of size m(p – 1) to one of its neighbors.
• Each node extracts the information meant for it from the
data received, and forwards the remaining (p – 2) pieces
of size m each to the next node.
• The algorithm terminates in p – 1 steps.
• The size of the message reduces by m at each step.
51. All-to-All Personalized Communication
on a Ring
All-to-all personalized communication on a six-node ring. The label of each
message is of the form {x,y}, where x is the label of the node that originally
owned the message, and y is the label of the node that is the final
destination of the message. The label ({x1,y1}, {x2,y2},…, {xn,yn}, indicates a
message that is formed by concatenating n individual messages.
52. All-to-All Personalized Communication
on a Ring: Cost
• We have p – 1 steps in all.
• In step i, the message size is m(p – i).
• The total time is given by:
• The tw term in this equation can be reduced by a factor of
2 by communicating messages in both directions.
53. All-to-All Personalized Communication
on a Mesh
• Each node first groups its p messages according to the
columns of their destination nodes.
• All-to-all personalized communication is performed
independently in each row with clustered messages of
size m√p.
• Messages in each node are sorted again, this time
according to the rows of their destination nodes.
• All-to-all personalized communication is performed
independently in each column with clustered messages
of size m√p.
54. All-to-All Personalized Communication
on a Mesh
The distribution of messages at the beginning of each phase of all-to-all personalized
communication on a 3 x 3 mesh. At the end of the second phase, node i has
messages ({0,i},…,{8,i}), where 0 ≤ i ≤ 8. The groups of nodes communicating together
in each phase are enclosed in dotted boundaries.
55. All-to-All Personalized Communication
on a Mesh: Cost
• Time for the first phase is identical to that in a ring with
√p processors, i.e., (ts + twmp/2)(√p – 1).
• Time in the second phase is identical to the first phase.
Therefore, total time is twice of this time, i.e.,
• It can be shown that the time for rearrangement is less
much less than this communication time.
56. All-to-All Personalized Communication
on a Hypercube
• Generalize the mesh algorithm to log p steps.
• At any stage in all-to-all personalized communication,
every node holds p packets of size m each.
• While communicating in a particular dimension, every
node sends p/2 of these packets (consolidated as one
message).
• A node must rearrange its messages locally before each
of the log p communication steps.
58. All-to-All Personalized Communication
on a Hypercube: Cost
• We have log p iterations and mp/2 words are
communicated in each iteration. Therefore, the cost is:
• This is not optimal!
59. All-to-All Personalized Communication
on a Hypercube: Optimal Algorithm
• Each node simply performs p – 1 communication steps,
exchanging m words of data with a different node in
every step.
• A node must choose its communication partner in each
step so that the hypercube links do not suffer
congestion.
• In the jth
communication step, node i exchanges data with
node (i XOR j).
• In this schedule, all paths in every communication step
are congestion-free, and none of the bidirectional links
carry more than one message in the same direction.
61. All-to-All Personalized Communication
on a Hypercube: Optimal Algorithm
A procedure to perform all-to-all personalized communication on a d-
dimensional hypercube. The message Mi,j initially resides on node i
and is destined for node j.
62. All-to-All Personalized Communication on a
Hypercube: Cost Analysis of Optimal
Algorithm
• There are p – 1 steps and each step involves non-
congesting message transfer of m words.
• We have:
• This is asymptotically optimal in message size.
63. Circular Shift
• A special permutation in which node i sends a data
packet to node (i + q) mod p in a p-node ensemble
(0 ≤ q ≤ p).
64. Circular Shift on a Mesh
• The implementation on a ring is rather intuitive. It can be
performed in min{q,p – q} neighbor communications.
• Mesh algorithms follow from this as well. We shift in one
direction (all processors) followed by the next direction.
• The associated time has an upper bound of:
65. Circular Shift on a Mesh
The communication steps in a circular 5-shift on a 4 x 4 mesh.
66. Circular Shift on a Hypercube
• Map a linear array with 2d
nodes onto a d-dimensional
hypercube.
• To perform a q-shift, we expand q as a sum of distinct
powers of 2.
• If q is the sum of s distinct powers of 2, then the circular
q-shift on a hypercube is performed in s phases.
• The time for this is upper bounded by:
• If E-cube routing is used, this time can be reduced to
67. Circular Shift on a Hypercube
The mapping of an eight-node linear array onto a three-dimensional hypercube
to perform a circular 5-shift as a combination of a 4-shift and a 1-shift.
68. Circular Shift on a Hypercube
Circular q-shifts on an 8-node hypercube for 1 ≤ q < 8.
69. Improving Performance of Operations
• Splitting and routing messages into parts: If the message
can be split into p parts, a one-to-all broadcast can be
implemented as a scatter operation followed by an all-to-
all broadcast operation. The time for this is:
• All-to-one reduction can be performed by performing all-
to-all reduction (dual of all-to-all broadcast) followed by a
gather operation (dual of scatter).
70. Improving Performance of Operations
• Since an all-reduce operation is semantically equivalent
to an all-to-one reduction followed by a one-to-all
broadcast, the asymptotically optimal algorithms for
these two operations can be used to construct a similar
algorithm for the all-reduce operation.
• The intervening gather and scatter operations cancel
each other. Therefore, an all-reduce operation requires
an all-to-all reduction and an all-to-all broadcast.