A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs

• 成果类型: Article
• 署名作者: Gouveia, Joao; Laurent, Monique; Parrilo, Pablo A.; Thomas, Rekha
• 署名单位: University of Washington; University of Washington Seattle; Universidade de Coimbra; Centrum Wiskunde & Informatica (CWI); Tilburg University; Massachusetts Institute of Technology (MIT)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-010-0425-z
• 发表日期: 2012
• 页码: 203-225
• 关键词: relaxations; REPRESENTATIONS; polytopes

摘要

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 Lovasz.