A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs
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Author(s)
Gouveia, João
Laurent, Monique
Parrilo, Pablo A.
Thomas, Rekha
Date Issued
October 2010
Journal
Mathematical programming
Publisher
Springer
Citation
Gouveia, João et al. “A New Semidefinite Programming Hierarchy for Cycles in Binary Matroids and Cuts in Graphs.” Mathematical Programming (2010) : 1-23-23. Print.
Version
Final published version
Abstract
The theta bodies of a polynomial ideal are a series of semidefinite programming relaxations of the convex hull of the real variety of the ideal. In this paper we construct the theta bodies of the vanishing ideal of cycles in a binary matroid. Applied to cuts in graphs, this yields a new hierarchy of semidefinite programming relaxations of the cut polytope of the graph. If the binary matroid avoids certain minors we can characterize when the first theta body in the hierarchy equals the cycle polytope of the matroid. Specialized to cuts in graphs, this result solves a problem posed by Lovász.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution Noncommercial License
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DOI of Published Version
https://doi.org/10.1007/s10107-010-0425-z
