Binary positive semidefinite matrices and associated integer polytopes

Letchford, A N and Sorensen, M M (2008) Binary positive semidefinite matrices and associated integer polytopes. In: Integer Programming and Combinatorial Optimization. Lecture Notes in Computer Science . Springer, ITA, pp. 125-139. ISBN 3540688862

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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 max-cut problem, by showing that the so-called k-gonal inequalities define a polytope.

Item Type:
Contribution in Book/Report/Proceedings
Additional Information:
The full version of this paper appeared as: A.N. Letchford & M.M. Sørensen (2012) Binary positive semidefinite matrices and associated integer polytopes. Math. Program., 131(1), 253-271.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
?? MANAGEMENT SCIENCEDISCIPLINE-BASED RESEARCH ??
ID Code:
46938
Deposited By:
Deposited On:
11 Jul 2011 20:09
Refereed?:
Yes
Published?:
Published
Last Modified:
17 Sep 2023 03:43