Parallel network simplex algorithm for the minimum cost flow problem

In this work, we contribute a parallel implementation of the network simplex algorithm that is used for the solution of minimum cost flow problem. In the network simplex algorithm, finding an entering arc requires searching through many arcs to decide which one should be included in the spanning tre...

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Bibliographic Details
Published in:Concurrency and computation Vol. 34; no. 4
Main Authors: Kara, Gökçehan, Özturan, Can
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc 15.02.2022
Subjects:
Algorithms
block search pivoting rule
Graph theory
Minimum cost
minimum cost flow problem
network simplex algorithm
shared memory parallelism
Simplex method
vectorization
ISSN:1532-0626, 1532-0634
Online Access:Get full text
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Summary:In this work, we contribute a parallel implementation of the network simplex algorithm that is used for the solution of minimum cost flow problem. In the network simplex algorithm, finding an entering arc requires searching through many arcs to decide which one should be included in the spanning tree solution on the next iteration. We propose finding the entering arc in parallel as it often takes the majority of the execution time. A usual strategy is to pick the arc violating the optimality the most out of all possible candidates. Scanning all arcs can take quite some time, so it is common to consider only a fixed number of arcs which is referred as the block search pivoting rule. Arc scans can easily be done in parallel to find the best candidate as the calculations are independent of each other. We used shared memory parallelism using OpenMP along with vectorization using AVX instructions. We also tried adjusting block sizes to increase the parallel portion of the algorithm. Our dataset consists of various natural and synthetic graphs with sizes up to a billion arc. Our experiments show speedups up to four are possible, though they are typically lower.
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ISSN:1532-0626
1532-0634
DOI:10.1002/cpe.6659