On the Tightening of the Standard SDP for Vertex Cover with $ell_1$ Inequalities
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چکیده
We show that the integrality gap of the standard SDP for VERTEX COVER on instances of n vertices remains 2− o(1) even after the addition of all hypermetric inequalities. Our lower bound requires new insights into the structure of SDP solutions behaving like l1 metric spaces when one point is removed. We also show that the addition of all l1 inequalities eliminates any solutions that are not convex combination of integral solutions. Consequently, we provide the strongest possible separation between hypermetrics and l1 inequalities with respect to the tightening of the standard SDP for VERTEX COVER.
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تاریخ انتشار 2009