Improved Approximation Algorithms for Projection Games

TL;DR

This paper presents new approximation algorithms for projection games, including a polynomial-time algorithm, a sub-exponential time algorithm for smooth cases, and a PTAS for planar graphs, advancing the field of approximation algorithms.

Contribution

It introduces several improved approximation algorithms for projection games, including a PTAS for planar graphs and tighter bounds for smooth cases, enhancing previous results.

Findings

Improved polynomial-time approximation algorithm over previous best.

A sub-exponential time algorithm with tighter approximation for smooth projection games.

A PTAS for projection games on planar graphs with a tight lower bound.

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, Hajiaghayi and Karloff. 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.