Binary positive semidefinite matrices and associated integer polytopes

Authors:
Adam N. Letchford;Michael M. SØrensen
Affiliations:
Department of Management Science, Lancaster University, Lancaster, United Kingdom;CORAL & Department of Business Studies, Aarhus School of Business, University of Aarhus, Denmark
Venue:
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Year:
2008

Citing 8
Cited 3

On the cut polytope

Mathematical Programming: Series A and B
The Boolean quadric polytope: some characteristics, facets and relatives

Mathematical Programming: Series A and B
Facets of the clique partitioning polytope

Mathematical Programming: Series A and B
Clique-web facets for multicut polytopes

Mathematics of Operations Research
Facets for the cut cone I

Mathematical Programming: Series A and B
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Journal of the ACM (JACM)
Semidefinite programming in combinatorial optimization

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Semidefinite programming relaxations for graph coloring and maximal clique problems

Mathematical Programming: Series A and B

The Chvátal-Gomory Closure of a Strictly Convex Body

Mathematics of Operations Research
The chvátal-gomory closure of an ellipsoid is a polyhedron

IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Gap inequalities for the max-cut problem: a cutting-plane algorithm

ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and well-known integer polytopes -- the cut, boolean quadric, multicut and clique partitioning polytopes -- are shown to arise as projections of binary psd polytopes. Finally, we present various valid inequalities for binary psd polytopes, and show how they relate to inequalities known for the simpler polytopes mentioned. Along the way, we answer an open question in the literature on the maxcut problem, by showing that the so-called k-gonal inequalities define a polytope.