On the effectiveness of the linear programming relaxation of the 0-1 multi-commodity minimum cost network flow problem

Dae S. Choi, In Chan Choi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Several studies have reported that the linear program relaxation of integer multi-commodity network flow problems often provides integer optimal solutions. We explore this phenomenon with a 0-1 multi-commodity network with mutual arc capacity constraints. Characteristics of basic solutions in the linear programming relaxation problem of the 0-1 multi-commodity problem are identified. Specifically, necessary conditions for a linear programming relaxation to have a non-integer solution are presented. Based on the observed characteristics, a simple illustrative example problem is constructed to show that its LP relaxation problem has integer optimal solutions with a relatively high probability. Furthermore, to investigate whether or not and under what conditions this tendency applies to large-sized problems, we have carried out computational experiments by using randomly generated problem instances. The results of our computational experiment indicate that there exists a narrow band of arc density in which the 0-1 multi-commodity problems possess no integer optimal solutions.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages517-526
Number of pages10
Volume4112 LNCS
Publication statusPublished - 2006 Oct 16
Event12th Annual International Conference on Computing and Combinatorics, COCOON 2006 - Taipei, Taiwan, Province of China
Duration: 2006 Aug 152006 Aug 18

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4112 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other12th Annual International Conference on Computing and Combinatorics, COCOON 2006
CountryTaiwan, Province of China
CityTaipei
Period06/8/1506/8/18

Fingerprint

Linear Programming
Minimum Cost Flow
Network Flow Problem
Linear Programming Relaxation
Linear programming
Costs and Cost Analysis
Costs
Experiments
Integer
Optimal Solution
Computational Experiments
Arc of a curve
LP Relaxation
Multicommodity Flow
Capacity Constraints
Linear Program
Necessary Conditions

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Choi, D. S., & Choi, I. C. (2006). On the effectiveness of the linear programming relaxation of the 0-1 multi-commodity minimum cost network flow problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4112 LNCS, pp. 517-526). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4112 LNCS).

On the effectiveness of the linear programming relaxation of the 0-1 multi-commodity minimum cost network flow problem. / Choi, Dae S.; Choi, In Chan.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4112 LNCS 2006. p. 517-526 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4112 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Choi, DS & Choi, IC 2006, On the effectiveness of the linear programming relaxation of the 0-1 multi-commodity minimum cost network flow problem. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4112 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4112 LNCS, pp. 517-526, 12th Annual International Conference on Computing and Combinatorics, COCOON 2006, Taipei, Taiwan, Province of China, 06/8/15.
Choi DS, Choi IC. On the effectiveness of the linear programming relaxation of the 0-1 multi-commodity minimum cost network flow problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4112 LNCS. 2006. p. 517-526. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Choi, Dae S. ; Choi, In Chan. / On the effectiveness of the linear programming relaxation of the 0-1 multi-commodity minimum cost network flow problem. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4112 LNCS 2006. pp. 517-526 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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