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Proving integrality gaps for linear relaxations of NP optimization problems is a difficult task and usually undertaken on a case-by-case basis. We initiate a more systematic approach. We prove an integrality gap of 2 − o(1) for three families of linear relaxations for VERTEX COVER, and our methods seem relevant to other problems as well.doi:10.1109/sfcs.2002.1181954 dblp:conf/focs/AroraBL02 fatcat:swdn6r3vebcljhe4k5om6b2p2i