Vertex Cover Resists SDPs Tightened by Local Hypermetric Inequalities

We consider the standard semidefinite programming (SDP) relaxation for vertex cover to which all hypermetric inequalities supported on at most k vertices have been added. We show that the integrality gap for such SDPs remains 2 - o(1) as long as k = O( p log n/ log log n). This extends successive results by Kleinberg-Goemans, Charikar and Hatami et al. which analyzed integrality gaps of the standard vertex cover SDP relaxation as well as for SDPs tightened using triangle and pentagonal inequalities. Our result is complementary but incomparable to a recent result by Georgiou et al. proving integrality gaps for vertex cover SDPs in the Lov

• Type: Conference
• Year: 2008
• Where: IPCO
• Authors: Konstantinos Georgiou, Avner Magen, Iannis Tourlakis
• Keywords: IPCO 2008, Optimization, SDPs, Vertex Cover, Vertex Cover Sdps