Improved Approximation Algorithms for Projection Games

Abstract

The projection games (aka Label Cover) problem is of great importance to the field of approximation algorithms, since most of the NP-hardness of approximation results we know today are reductions from Label Cover. In this paper we design several approximation algorithms for projection games: (1) A polynomial-time approximation algorithm that improves on the previous best approximation by Charikar et al. (Algorithmica 61(1):190–206, 2011). (2) A sub-exponential time algorithm with much tighter approximation for the case of smooth projection games. (3) A polynomial-time approximation scheme (PTAS) for projection games on planar graphs and a tight running time lower bound for such approximation schemes. The conference version of this paper had only the PTAS but not the running time lower bound.