Bazzi, AbbasFiorini, SamuelPokutta, SebastianSvensson, Ola2019-06-182019-06-182019-06-182019-02-0110.1287/moor.2017.0918https://infoscience.epfl.ch/handle/20.500.14299/157553WOS:000459418400008The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev [Khot S, Regev O (2008) Vertex cover might be hard to approximate to within 2 - epsilon. J. Comput. System Sci. 74(3): 335-349] proved that the problem is NP-hard to approximate within a factor 2- epsilon, assuming the unique games conjecture (UGC). This is tight because the problem has an easy 2-approximation algorithm. Without resorting to the UGC, the best inapproximability result for the problem is due to Dinur and Safra [Dinur I, Safra S (2005) On the hardness of approximating minimum vertex cover. Ann. Math. 162(1):439-485]: vertex cover is NP-hard to approximate within a factor 1.3606.We prove the following unconditional result about linear programming (LP) relaxations of the problem: every LP relaxation that approximates the vertex cover within a factor 2 - epsilon has super-polynomially many inequalities. As a direct consequence of our methods, we also establish that LP relaxations (as well as semidefinite programming relaxations) that approximate the independent set problem within any constant factor have a super-polynomial size.Operations Research & Management ScienceMathematics, AppliedMathematicsextended formulationshardness of approximationindependent setlinear programmingvertex coverintegrality gapslower boundsrelaxationsoptimizationhardnesstext::journal::journal article::research article