### Abstract

Given a finite set X and a family of "feasible" subsets F of X, the 0-1 polytope P (F is defined as the convex hull of all the characteristic vectors of members of F We show that under a certain assumption a special type of face of P(F) is equivalent to the ideal polytope of some pseudo-ordered set. Examples of families satisfying the assumption are those related to the maximum stable set problem, set packing and set partitioning problems, and vertex coloring problem. Using this fact, we propose a new heuristic for such problems and give results of our preliminary computational experiments for the maximum stable set problem.

Original language | English |
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Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Mathematical Programming |

Volume | 71 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1995 Nov |

Externally published | Yes |

### Keywords

- 0-1 polytopes
- Heuristic
- Ideal polytopes
- Maximum stable set problem

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

Ikebe, Y. T., & Tamura, A. (1995). Ideal polytopes and face structures of some combinatorial optimization problems.

*Mathematical Programming*,*71*(1), 1-15. https://doi.org/10.1007/BF01592241