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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| Veröffentlicht in: | Concurrency and computation Jg. 34; H. 4 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Özturan, Can Kara, Gökçehan |
| Author_xml | – sequence: 1 givenname: Gökçehan orcidid: 0000-0002-7104-4743 surname: Kara fullname: Kara, Gökçehan email: gokcehan.kara@boun.edu.tr organization: Boğaziçi University – sequence: 2 givenname: Can orcidid: 0000-0003-0465-2519 surname: Özturan fullname: Özturan, Can organization: Boğaziçi University |
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| Cites_doi | 10.1137/17M1137553 10.1145/3280847 10.1016/j.entcs.2011.06.003 10.24963/ijcai.2019/414 10.1145/2145816.2145840 10.1080/03155986.1979.11731713 10.1007/978-3-319-89920-6_42 10.1287/opre.42.1.65 10.1016/j.ejor.2016.11.024 10.1145/320924.320927 10.1145/322063.322070 10.1109/SPDP.1993.395504 10.1145/1465482.1465560 10.1007/BF01580379 10.1109/DFM.2012.10 10.1007/BFb0121089 10.1145/321752.321754 10.1504/IJOR.2014.061773 10.1145/42411.42415 10.1515/9781400884179 10.1016/0167-6377(90)90026-2 10.1016/j.cie.2012.04.016 10.1109/99.660313 10.1090/dimacs/012 10.1109/ACCESS.2018.2883251 10.1504/WRITR.2019.097836 10.1007/BF01584319 10.2298/YJOR121120001S 10.1287/mnsc.24.1.1 10.1080/10556788.2014.895828 10.1002/net.3230200704 10.1109/ICCA.2019.8899971 10.1007/s00500-019-03951-2 10.1007/978-3-319-55702-1_84 10.1007/978-3-030-48439-2_92 10.1016/j.cor.2012.08.018 10.1007/s11227-020-03227-9 |
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| SubjectTerms | Algorithms block search pivoting rule Graph theory Minimum cost minimum cost flow problem network simplex algorithm shared memory parallelism Simplex method vectorization |
| Title | Parallel network simplex algorithm for the minimum cost flow problem |
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