Binary positive semidefinite matrices and associated integer polytopes

Letchford, A N and Sorensen, M M (2012) Binary positive semidefinite matrices and associated integer polytopes. Mathematical Programming, 131 (1-2). pp. 253-271. ISSN 0025-5610

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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.

Item Type:
Journal Article
Journal or Publication Title:
Mathematical Programming
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This is the full journal version of a paper that appeared as a chapter in the 2008 IPCO volume.
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Deposited On:
04 Oct 2011 15:12
Last Modified:
13 Feb 2023 00:12