### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Mathematics(all)
- Safety, Risk, Reliability and Quality
- Management Science and Operations Research
- Software
- Computer Graphics and Computer-Aided Design
- Computer Science(all)

### Cite this

*Mathematical Programming*,

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

**Ideal polytopes and face structures of some combinatorial optimization problems.** / Ikebe, Yoshiko T.; Tamura, Akihisa.

Research output: Contribution to journal › Article

*Mathematical Programming*, vol. 71, no. 1, pp. 1-15. https://doi.org/10.1007/BF01592241

}

TY - JOUR

T1 - Ideal polytopes and face structures of some combinatorial optimization problems

AU - Ikebe, Yoshiko T.

AU - Tamura, Akihisa

PY - 1995/11

Y1 - 1995/11

N2 - 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.

AB - 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.

KW - 0-1 polytopes

KW - Heuristic

KW - Ideal polytopes

KW - Maximum stable set problem

UR - http://www.scopus.com/inward/record.url?scp=0029194763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029194763&partnerID=8YFLogxK

U2 - 10.1007/BF01592241

DO - 10.1007/BF01592241

M3 - Article

AN - SCOPUS:0029194763

VL - 71

SP - 1

EP - 15

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -