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, Hajiaghayi and Karloff [7]. 2. A sub-exponential time algorithm with much tighter approximation for the case of smooth projection games. 3. A PTAS for planar graphs.
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