A faster polynomial algorithm for the constrained maximum flow problem
The constrained maximum flow problem is a variant of the classical maximum flow problem in which the flow from a source node to a sink node is maximized in a directed capacitated network with arc costs subject to the constraint that the total cost of flow should be within a budget. It is important t...
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| Published in | Computers & operations research Vol. 39; no. 11; pp. 2634 - 2641 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.11.2012
Elsevier Pergamon Press Inc |
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| Online Access | Get full text |
| ISSN | 0305-0548 1873-765X 0305-0548 |
| DOI | 10.1016/j.cor.2012.01.010 |
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| Abstract | The constrained maximum flow problem is a variant of the classical maximum flow problem in which the flow from a source node to a sink node is maximized in a directed capacitated network with arc costs subject to the constraint that the total cost of flow should be within a budget. It is important to study this problem because it has important applications, such as in logistics, telecommunications and computer networks; and because it is related to variants of classical problems such as the constrained shortest path problem, constrained transportation problem, or constrained assignment problem, all of which have important applications as well. In this research, we present an O(n2mlog(nC)) time cost scaling algorithm and compare its empirical performance against the two existing polynomial combinatorial algorithms for the problem: the capacity scaling and the double scaling algorithms. We show that the cost scaling algorithm is on average 25 times faster than the double scaling algorithm, and 32 times faster than the capacity scaling algorithm. |
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| AbstractList | The constrained maximum flow problem is a variant of the classical maximum flow problem in which the flow from a source node to a sink node is maximized in a directed capacitated network with arc costs subject to the constraint that the total cost of flow should be within a budget. It is important to study this problem because it has important applications, such as in logistics, telecommunications and computer networks; and because it is related to variants of classical problems such as the constrained shortest path problem, constrained transportation problem, or constrained assignment problem, all of which have important applications as well. In this research, we present an O(n2mlog(nC)) time cost scaling algorithm and compare its empirical performance against the two existing polynomial combinatorial algorithms for the problem: the capacity scaling and the double scaling algorithms. We show that the cost scaling algorithm is on average 25 times faster than the double scaling algorithm, and 32 times faster than the capacity scaling algorithm. The constrained maximum flow problem is a variant of the classical maximum flow problem in which the flow from a source node to a sink node is maximized in a directed capacitated network with arc costs subject to the constraint that the total cost of flow should be within a budget. It is important to study this problem because it has important applications, such as in logistics, telecommunications and computer networks; and because it is related to variants of classical problems such as the constrained shortest path problem, constrained transportation problem, or constrained assignment problem, all of which have important applications as well. In this research, we present an O(n^sup 2^m log(nC)) time cost scaling algorithm and compare its empirical performance against the two existing polynomial combinatorial algorithms for the problem: the capacity scaling and the double scaling algorithms. We show that the cost scaling algorithm is on average 25 times faster than the double scaling algorithm, and 32 times faster than the capacity scaling algorithm. [PUBLICATION ABSTRACT] The constrained maximum flow problem is a variant of the classical maximum flow problem in which the flow from a source node to a sink node is maximized in a directed capacitated network with arc costs subject to the constraint that the total cost of flow should be within a budget. It is important to study this problem because it has important applications, such as in logistics, telecommunications and computer networks; and because it is related to variants of classical problems such as the constrained shortest path problem, constrained transportation problem, or constrained assignment problem, all of which have important applications as well. In this research, we present an O ( n 2 m log ( nC ) ) time cost scaling algorithm and compare its empirical performance against the two existing polynomial combinatorial algorithms for the problem: the capacity scaling and the double scaling algorithms. We show that the cost scaling algorithm is on average 25 times faster than the double scaling algorithm, and 32 times faster than the capacity scaling algorithm. |
| Author | Çalışkan, Cenk |
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| Keywords | Scaling Minimum cost network flow Network flows Computational complexity Maximum flow Costs Network flow Assignment problem Combinatorial problem Empirical method Shortest path Graph theory Distributed system Combinatorial optimization Source sink relationship Source flow Transportation problem Computer network Time average Telecommunication network Budget Capacity constraint Optimal flow Logistics |
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| References | Thorup (bib19) 2000; 30 Ahuja, Mehlhorn, Orlin, Tarjan (bib1) 1990; 37 Malek-Zavarei, Frisch (bib15) 1971; 14 Gabow, Tarjan (bib10) 1989; 18 Goldberg, Tarjan (bib12) 1990; 15 Çalışkan (bib5) 2008; 35 Ahuja, Orlin (bib2) 1995; 25 Röck (bib17) 1980 Bertsekas DP. A distributed algorithm for the assignment problem. Working Paper. Laboratory for Information and Decision Systems. Cambridge, MA: MIT; 1979. Johnson (bib14) 1982; 15 Çalışkan (bib7) 2011; 210 Ahuja, Magnanti, Orlin (bib3) 1993 Fulkerson (bib9) 1959; 5 Hagerup T. Improved shortest paths in the word RAM. In: 27th international colloquium on automata, languages, and programming, Geneva, Switzerland, 2000. p. 61–72. Çalışkan (bib6) 2009; 53 Ford, Fulkerson (bib8) 1956; 8 Thorup (bib20) 2003 Raman (bib16) 1996; vol. 1136 Tardos (bib18) 1985; 5 Goldberg, Tarjan (bib11) 1987 Raman (10.1016/j.cor.2012.01.010_bib16) 1996; vol. 1136 Tardos (10.1016/j.cor.2012.01.010_bib18) 1985; 5 Ford (10.1016/j.cor.2012.01.010_bib8) 1956; 8 Ahuja (10.1016/j.cor.2012.01.010_bib1) 1990; 37 10.1016/j.cor.2012.01.010_bib13 Malek-Zavarei (10.1016/j.cor.2012.01.010_bib15) 1971; 14 10.1016/j.cor.2012.01.010_bib4 Goldberg (10.1016/j.cor.2012.01.010_bib11) 1987 Goldberg (10.1016/j.cor.2012.01.010_bib12) 1990; 15 Çalışkan (10.1016/j.cor.2012.01.010_bib6) 2009; 53 Röck (10.1016/j.cor.2012.01.010_bib17) 1980 Thorup (10.1016/j.cor.2012.01.010_bib20) 2003 Çalışkan (10.1016/j.cor.2012.01.010_bib5) 2008; 35 Fulkerson (10.1016/j.cor.2012.01.010_bib9) 1959; 5 Ahuja (10.1016/j.cor.2012.01.010_bib3) 1993 Gabow (10.1016/j.cor.2012.01.010_bib10) 1989; 18 Ahuja (10.1016/j.cor.2012.01.010_bib2) 1995; 25 Çalışkan (10.1016/j.cor.2012.01.010_bib7) 2011; 210 Johnson (10.1016/j.cor.2012.01.010_bib14) 1982; 15 Thorup (10.1016/j.cor.2012.01.010_bib19) 2000; 30 |
| References_xml | – start-page: 7 year: 1987 end-page: 18 ident: bib11 article-title: Solving minimum cost flow problem by successive approximation publication-title: Proceedings of the 19th ACM symposium on the theory of computing – volume: vol. 1136 start-page: 121 year: 1996 end-page: 137 ident: bib16 article-title: Priority queues: small monotone and trans-dichotomous publication-title: Proceedings of the fourth annual European symposium on algorithms. Lecture notes in computer science – volume: 210 start-page: 137 year: 2011 end-page: 147 ident: bib7 article-title: A specialized network simplex algorithm for the constrained maximum flow problem publication-title: Eur J Operat Res – volume: 5 start-page: 473 year: 1959 end-page: 483 ident: bib9 article-title: Increasing the capacity of a network: the parametric budget problem publication-title: Manage Sci – volume: 37 start-page: 213 year: 1990 end-page: 223 ident: bib1 article-title: Faster algorithms for the shortest path problem publication-title: J ACM – volume: 25 start-page: 89 year: 1995 end-page: 98 ident: bib2 article-title: A capacity scaling algorithm for the constrained maximum flow problem publication-title: Networks – reference: Bertsekas DP. A distributed algorithm for the assignment problem. Working Paper. Laboratory for Information and Decision Systems. Cambridge, MA: MIT; 1979. – volume: 35 start-page: 1138 year: 2008 end-page: 1150 ident: bib5 article-title: A double scaling algorithm for the constrained maximum flow problem publication-title: Comput Operat Res – volume: 18 start-page: 1013 year: 1989 end-page: 1036 ident: bib10 article-title: Faster scaling algorithms for network problems publication-title: SIAM J Comput – volume: 15 start-page: 430 year: 1990 end-page: 466 ident: bib12 article-title: Finding minimum cost flow circulations by successive approximation publication-title: Math Operat Res – volume: 53 start-page: 229 year: 2009 end-page: 230 ident: bib6 article-title: On a capacity scaling algorithm for the constrained maximum flow problem publication-title: Networks – volume: 5 start-page: 155 year: 1985 end-page: 247 ident: bib18 article-title: A strongly polynomial minimum cost circulation algorithm publication-title: Combinatorica – volume: 15 start-page: 295 year: 1982 end-page: 309 ident: bib14 article-title: A priority queue in which initialization and queue operations take publication-title: Math Syst Theory – start-page: 149 year: 2003 end-page: 158 ident: bib20 article-title: Integer priority queues with decrease key in constant time and the single source shortest paths problem publication-title: Proceedings of the 35th annual ACM symposium on theory of computing (STOC), San Diego, CA – volume: 30 start-page: 86 year: 2000 end-page: 109 ident: bib19 article-title: On RAM priority queues publication-title: SIAM J Comput – reference: Hagerup T. Improved shortest paths in the word RAM. In: 27th international colloquium on automata, languages, and programming, Geneva, Switzerland, 2000. p. 61–72. – start-page: 181 year: 1980 end-page: 191 ident: bib17 article-title: Scaling techniques for minimal cost network flows publication-title: Discrete structures and algorithms – volume: 14 start-page: 549 year: 1971 end-page: 560 ident: bib15 article-title: A constrained maximum flow problem publication-title: Int J Control – year: 1993 ident: bib3 article-title: Network flows: theory, algorithms and applications – volume: 8 start-page: 399 year: 1956 end-page: 404 ident: bib8 article-title: Maximum flow through a network publication-title: Can J Math – start-page: 7 year: 1987 ident: 10.1016/j.cor.2012.01.010_bib11 article-title: Solving minimum cost flow problem by successive approximation – volume: 30 start-page: 86 year: 2000 ident: 10.1016/j.cor.2012.01.010_bib19 article-title: On RAM priority queues publication-title: SIAM J Comput doi: 10.1137/S0097539795288246 – volume: 25 start-page: 89 year: 1995 ident: 10.1016/j.cor.2012.01.010_bib2 article-title: A capacity scaling algorithm for the constrained maximum flow problem publication-title: Networks doi: 10.1002/net.3230250207 – start-page: 181 year: 1980 ident: 10.1016/j.cor.2012.01.010_bib17 article-title: Scaling techniques for minimal cost network flows – ident: 10.1016/j.cor.2012.01.010_bib4 – volume: 53 start-page: 229 issue: 3 year: 2009 ident: 10.1016/j.cor.2012.01.010_bib6 article-title: On a capacity scaling algorithm for the constrained maximum flow problem publication-title: Networks doi: 10.1002/net.20263 – volume: 15 start-page: 430 year: 1990 ident: 10.1016/j.cor.2012.01.010_bib12 article-title: Finding minimum cost flow circulations by successive approximation publication-title: Math Operat Res doi: 10.1287/moor.15.3.430 – volume: 15 start-page: 295 year: 1982 ident: 10.1016/j.cor.2012.01.010_bib14 article-title: A priority queue in which initialization and queue operations take O(loglogD) time publication-title: Math Syst Theory doi: 10.1007/BF01786986 – volume: 8 start-page: 399 year: 1956 ident: 10.1016/j.cor.2012.01.010_bib8 article-title: Maximum flow through a network publication-title: Can J Math doi: 10.4153/CJM-1956-045-5 – volume: 5 start-page: 473 issue: 1 year: 1959 ident: 10.1016/j.cor.2012.01.010_bib9 article-title: Increasing the capacity of a network: the parametric budget problem publication-title: Manage Sci – volume: vol. 1136 start-page: 121 year: 1996 ident: 10.1016/j.cor.2012.01.010_bib16 article-title: Priority queues: small monotone and trans-dichotomous – volume: 14 start-page: 549 issue: 3 year: 1971 ident: 10.1016/j.cor.2012.01.010_bib15 article-title: A constrained maximum flow problem publication-title: Int J Control doi: 10.1080/00207177108932064 – year: 1993 ident: 10.1016/j.cor.2012.01.010_bib3 – volume: 210 start-page: 137 issue: 2 year: 2011 ident: 10.1016/j.cor.2012.01.010_bib7 article-title: A specialized network simplex algorithm for the constrained maximum flow problem publication-title: Eur J Operat Res doi: 10.1016/j.ejor.2010.10.018 – volume: 18 start-page: 1013 year: 1989 ident: 10.1016/j.cor.2012.01.010_bib10 article-title: Faster scaling algorithms for network problems publication-title: SIAM J Comput doi: 10.1137/0218069 – volume: 35 start-page: 1138 issue: 4 year: 2008 ident: 10.1016/j.cor.2012.01.010_bib5 article-title: A double scaling algorithm for the constrained maximum flow problem publication-title: Comput Operat Res doi: 10.1016/j.cor.2006.07.009 – volume: 37 start-page: 213 year: 1990 ident: 10.1016/j.cor.2012.01.010_bib1 article-title: Faster algorithms for the shortest path problem publication-title: J ACM doi: 10.1145/77600.77615 – ident: 10.1016/j.cor.2012.01.010_bib13 doi: 10.1007/3-540-45022-X_7 – volume: 5 start-page: 155 year: 1985 ident: 10.1016/j.cor.2012.01.010_bib18 article-title: A strongly polynomial minimum cost circulation algorithm publication-title: Combinatorica doi: 10.1007/BF02579369 – start-page: 149 year: 2003 ident: 10.1016/j.cor.2012.01.010_bib20 article-title: Integer priority queues with decrease key in constant time and the single source shortest paths problem |
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| SubjectTerms | Algorithms Applied sciences Combinatorial analysis Comparative studies Computational complexity Computer science; control theory; systems Computer systems and distributed systems. User interface Constraints Costs Exact sciences and technology Flows in networks. Combinatorial problems Inventory control, production control. Distribution Logistics Maximum flow Minimum cost network flow Network flow problem Network flows Operational research and scientific management Operational research. Management science Operations research Polynomials Scaling Shortest-path problems Software Transportation problem Transportation problem (Operations research) |
| Title | A faster polynomial algorithm for the constrained maximum flow problem |
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