### 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 language | English |
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Title of host publication | Computing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings |

Publisher | Springer Verlag |

Pages | 517-526 |

Number of pages | 10 |

ISBN (Print) | 3540369252, 9783540369257 |

Publication status | Published - 2006 |

Event | 12th Annual International Conference on Computing and Combinatorics, COCOON 2006 - Taipei, Taiwan, Province of China Duration: 2006 Aug 15 → 2006 Aug 18 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4112 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th Annual International Conference on Computing and Combinatorics, COCOON 2006 |
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Country | Taiwan, Province of China |

City | Taipei |

Period | 06/8/15 → 06/8/18 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*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.