WHEN: 11.06.15 at 14:15
WHERE: Seminar Room, Arnimallee 2, FU Berlin

Speaker: Samuel Fiorini (UL Bruxelles)

No Small Linear Program Approximates Vertex Cover within a Factor 2-epsilon

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) 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 (2002): 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 vertex cover within a factor of 2-epsilon has super-polynomially many inequalities. As a direct consequence of our methods, we also establish that LP relaxations that approximate the independent set problem within any constant factor have super-polynomially many inequalities.

This is joint work with Abbas Bazzi, Sebastian Pokutta and Ola Svensson.