Volume 2 (2006) Article 2 pp. 19-51
Proving Integrality Gaps without Knowing the Linear Program
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.