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Binary positive semidefinite matrices and associated integer polytopes

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>02/2012
<mark>Journal</mark>Mathematical Programming
Issue number1-2
Volume131
Number of pages19
Pages (from-to)253-271
<mark>State</mark>Published
Early online date23/04/10
<mark>Original language</mark>English

Abstract

We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes.We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature—the cut, boolean quadric, multicut and clique partitioning polytopes—are faces of binary psd polytopes. Finally,we present some implications of these polyhedral relationships. In particular, we answer an open question in the literature on the max-cut problem, by showing that the rounded psd inequalities define a polytope.

Bibliographic note

This is the full journal version of a paper that appeared as a chapter in the 2008 IPCO volume.