 
Summary: Proving integrality gaps without knowing the linear program
Sanjeev Arora #
Princeton University
B’ela Bollob’as +#§
University of Memphis
L’aszl’o Lov’asz ¶
Microsoft Research
Abstract
Proving integrality gaps for linear relaxations of NP
optimization problems is a di#cult task and usually
undertaken on a casebycase basis. We initiate a
more systematic approach. We prove an integrality
gap of 2o(1) for three families of linear relaxations
for vertex cover, and our methods seem relevant to
other problems as well.
1 Introduction
Approximation algorithms for NPhard problems 
metric TSP, Vertex Cover, graph expansion, cut
problems, etc. often use a linear relaxation of the
problem (see Vazirani [19], Hochbaum [13]). For in
