Integrality in the multinetwork min‐cost equal‐flow problem
We consider the min‐cost flow problem on multiple networks defined on duplicates of the same directed graph. The problem is to compute feasible flows such that the sum of flow costs is minimized subject to network demands and coupling constraints that force identical flows on duplicate copies of the...
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| Published in | Networks Vol. 80; no. 3; pp. 267 - 273 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken, USA
John Wiley & Sons, Inc
01.10.2022
Wiley Subscription Services, Inc |
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| ISSN | 0028-3045 1097-0037 |
| DOI | 10.1002/net.22094 |
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| Abstract | We consider the min‐cost flow problem on multiple networks defined on duplicates of the same directed graph. The problem is to compute feasible flows such that the sum of flow costs is minimized subject to network demands and coupling constraints that force identical flows on duplicate copies of the same edge for a subset of “special” edges. We focus on whether such a problem has an integer optimal solution. For the case of integer capacities and demands and flow equality on a single edge, there is always an integer optimal solution and it can be found efficiently. For flow equality on multiple edges, we characterize the cases, with respect to the number of special edges and the number of networks, where if the graph is series‐parallel then an integer optimal solution exists for all possible capacity and cost functions. |
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| AbstractList | We consider the min‐cost flow problem on multiple networks defined on duplicates of the same directed graph. The problem is to compute feasible flows such that the sum of flow costs is minimized subject to network demands and coupling constraints that force identical flows on duplicate copies of the same edge for a subset of “special” edges. We focus on whether such a problem has an integer optimal solution. For the case of integer capacities and demands and flow equality on a single edge, there is always an integer optimal solution and it can be found efficiently. For flow equality on multiple edges, we characterize the cases, with respect to the number of special edges and the number of networks, where if the graph is series‐parallel then an integer optimal solution exists for all possible capacity and cost functions. |
| Author | Hassin, Refael Poznanski, Renata |
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| Copyright | 2022 The Authors. published by Wiley Periodicals LLC. 2022. This article is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| References | 2004; 43 2002; 2387 1962; 254 2013; 25 1993; 62 1986; 7 1988; 36 1999; 45 1979; 4 1983; 30 1988; 40 2014; 8 1985; 10 1998; 44 2009; 37 2022; 312 e_1_2_9_11_1 e_1_2_9_10_1 e_1_2_9_13_1 e_1_2_9_12_1 e_1_2_9_8_1 e_1_2_9_6_1 e_1_2_9_5_1 e_1_2_9_4_1 e_1_2_9_3_1 e_1_2_9_2_1 e_1_2_9_9_1 e_1_2_9_15_1 e_1_2_9_14_1 e_1_2_9_17_1 e_1_2_9_16_1 Ghouila‐Houri A. (e_1_2_9_7_1) 1962; 254 |
| References_xml | – volume: 30 start-page: 852 year: 1983 end-page: 865 article-title: Applying parallel computation algorithms in the design of serial algorithms publication-title: J. ACM – volume: 62 start-page: 1 year: 1993 end-page: 14 article-title: Series parallel composition of greedy linear programming problems publication-title: Math. Program. – volume: 40 start-page: 197 year: 1988 end-page: 204 article-title: On greedy algorithms for series parallel graphs publication-title: Math. Program. – volume: 44 start-page: 49 year: 1998 end-page: 67 article-title: An efficient lagrangean relaxation scheme for linear and integer equal flow problems publication-title: Optimization – volume: 45 start-page: 1440 year: 1999 end-page: 1455 article-title: Algorithms for the simple equal‐flow problem publication-title: Manag. Sci. – volume: 37 start-page: 245 year: 2009 end-page: 249 article-title: Integer equal flows publication-title: Oper. Res. Lett. – volume: 2387 start-page: 514 year: 2002 end-page: 524 – volume: 4 start-page: 414 year: 1979 end-page: 424 article-title: Combinatorial optimization with rational objective functions publication-title: Math. Oper. Res. – volume: 254 start-page: 1192 year: 1962 end-page: 1194 article-title: Characterisation des matrices totalement unimodulaires publication-title: C. R. Hebd. Seances Acad. Sci. – volume: 25 start-page: 2 year: 2013 end-page: 12 article-title: A network simplex algorithm for the equal flow problem on a generalized network publication-title: INFORMS J. Comput. – volume: 36 start-page: 107 year: 1988 end-page: 115 article-title: The equal‐flow problem publication-title: Eur. J. Oper. Res. – volume: 43 start-page: 153 year: 2004 end-page: 162 article-title: Minimum‐cost dynamic flows: The series‐parallel case publication-title: Networks – volume: 10 start-page: 117 year: 1985 end-page: 124 article-title: Minimum cost flow algorithms for series‐parallel networks publication-title: Discret. Appl. Math. – volume: 312 start-page: 691 year: 2022 end-page: 722 article-title: Robust minimum cost flow problem under consistent flow constraints publication-title: Ann. Oper. Res. – volume: 7 start-page: 379 year: 1986 end-page: 389 article-title: Efficient algorithms for optimization and selection on series‐parallel graphs publication-title: SIAM J. Alg. Discret. Meth. – volume: 8 start-page: 801 year: 2014 end-page: 809 article-title: An algorithm to solve the proportional network flow problem publication-title: Optim. Lett. – ident: e_1_2_9_12_1 doi: 10.1287/moor.4.4.414 – ident: e_1_2_9_9_1 doi: 10.1007/BF01580730 – ident: e_1_2_9_15_1 doi: 10.1287/ijoc.1110.0485 – ident: e_1_2_9_17_1 doi: 10.1007/3-540-45655-4_55 – volume: 254 start-page: 1192 year: 1962 ident: e_1_2_9_7_1 article-title: Characterisation des matrices totalement unimodulaires publication-title: C. R. Hebd. Seances Acad. Sci. – ident: e_1_2_9_2_1 doi: 10.1287/mnsc.45.10.1440 – ident: e_1_2_9_3_1 doi: 10.1016/0377-2217(88)90012-4 – ident: e_1_2_9_6_1 doi: 10.1007/s10479-021-04426-0 – ident: e_1_2_9_16_1 doi: 10.1007/s11590-013-0634-5 – ident: e_1_2_9_5_1 doi: 10.1016/0166-218X(85)90006-X – ident: e_1_2_9_8_1 doi: 10.1137/0607043 – ident: e_1_2_9_13_1 doi: 10.1145/2157.322410 – ident: e_1_2_9_10_1 doi: 10.1002/net.10112 – ident: e_1_2_9_11_1 doi: 10.1080/02331939808844399 – ident: e_1_2_9_4_1 doi: 10.1007/BF01585157 – ident: e_1_2_9_14_1 doi: 10.1016/j.orl.2009.03.006 |
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| Snippet | We consider the min‐cost flow problem on multiple networks defined on duplicates of the same directed graph. The problem is to compute feasible flows such that... |
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| SubjectTerms | computational complexity Cost function equal‐flow problem Graph theory Integers integral solutions min‐cost flow Reproduction (copying) Series (mathematics) |
| Title | Integrality in the multinetwork min‐cost equal‐flow problem |
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