Summary: Subexponential Algorithms for UNIQUE GAMES
and Related Problems
April 14, 2010
We give subexponential time approximation algorithms for UNIQUE GAMES and the SMALL-SET EXPAN-
SION. Specifically, for some absolute constant c, we give:
1. An exp(kn
)-time algorithm that, given as input a k-alphabet unique game on n variables that has
an assignment satisfying 1 - c
fraction of its constraints, outputs an assignment satisfying 1 -
fraction of the constraints.
2. An exp(n
/)-time algorithm that, given as input an n-vertex regular graph that has a set S of n
vertices with edge expansion at most c
, outputs a set S of at most n vertices with edge expansion
at most .
We also obtain a subexponential algorithm with improved approximation for MULTI CUT, as well as