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

Dae Sik 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 publicationComputing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings
PublisherSpringer Verlag
Pages517-526
Number of pages10
ISBN (Print)3540369252, 9783540369257
Publication statusPublished - 2006 Jan 1
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)0302-9743
ISSN (Electronic)1611-3349

Other

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

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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 Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings (pp. 517-526). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4112 LNCS). Springer Verlag.