文章基本信息

标题：On the Tightening of the Standard SDP for Vertex Cover with $ell_1$ Inequalities
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作者：Konstantinos Georgiou ; Avner Magen ; Iannis Tourlakis 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2009
卷号：4
页码：203-214
DOI：10.4230/LIPIcs.FSTTCS.2009.2319
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We show that the integrality gap of the standard SDP for \vc~on instances of $n$ vertices remains $2-o(1)$ even after the addition of \emph{all} hypermetric inequalities. Our lower bound requires new insights into the structure of SDP solutions behaving like $\ell_1$ metric spaces when one point is removed. We also show that the addition of all $\ell_1$ inequalities eliminates any solutions that are not convex combination of integral solutions. Consequently, we provide the strongest possible separation between hypermetrics and $\ell_1$ inequalities with respect to the tightening of the standard SDP for \vc.
关键词：Semidefinite Programming; Vertex Cover; Integrality Gap; Hypermetric Inequalities