Binary Positive Semidefinite Matrices and Associated Integer Polytopes

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, m...

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Bibliographic Details
Published inInteger Programming and Combinatorial Optimization pp. 125 - 139
Main Authors Letchford, Adam N., Sørensen, Michael M.
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Polyhedral combinatorics
semidefinite programming
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Summary: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 max-cut problem, by showing that the so-called k-gonal inequalities define a polytope.
ISBN:3540688862
9783540688860
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-68891-4_9