How to recycle your facets

Authors:
Samuel Fiorini
Affiliations:
Department of Mathematics, Université Libre de Bruxelles, CP 216, Bd du Triomphe, B-1050 Brussels, Belgium
Venue:
Discrete Optimization
Year:
2006

Citing 16
Cited 1

The complexity of facets resolved

Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
On the set covering polytope: I. all the facets with coefficients in {0, 1, 2}

Mathematical Programming: Series A and B
Facets and lifting procedures for the set covering polytope

Mathematical Programming: Series A and B
Random utility representation of binary choice probabilities: a new class of necessary conditions

Journal of Mathematical Psychology
On the facial structure of the set covering polytope dimensional linear programming

Mathematical Programming: Series A and B
Compositions of Graphs and Polyhedra IV: Acyclic Spanning Subgraphs

SIAM Journal on Discrete Mathematics
More facets from fences for linear ordering and acyclic subgraph polytopes

Discrete Applied Mathematics
Random utility representation of binary choice probabilities: critical graphs yielding critical necessary conditions

Journal of Mathematical Psychology
Anti-Hadamard matrices, coin weighing, threshold gates, and indecomposable hypergraphs

Journal of Combinatorial Theory Series A
On the monotonization of polyhedra

Mathematical Programming: Series A and B
New Facets of the Linear Ordering Polytope

SIAM Journal on Discrete Mathematics
Determining the automorphism group of the linear ordering polytope

Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
The Strongest Facets of the Acyclic Subgraph Polytope Are Unknown

Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
A combinatorial study of partial order polytopes

European Journal of Combinatorics
Lower Bound for the Maximal Number of Facets of a 0/1 Polytope

Discrete & Computational Geometry
0, 1/2-Cuts and the Linear Ordering Problem: Surfaces That Define Facets

SIAM Journal on Discrete Mathematics

Weighted graphs defining facets: A connection between stable set and linear ordering polytopes

Discrete Optimization

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Abstract

We show how to transform any inequality defining a facet of some 0/1-polytope into an inequality defining a facet of the acyclic subgraph polytope. While this facet-recycling procedure can potentially be used to construct 'nasty' facets, it can also be used to better understand and extend the polyhedral theory of the acyclic subgraph and linear ordering problems.