 
Summary: Subexponential Algorithms for UNIQUE GAMES
and Related Problems
Sanjeev Arora
Boaz Barak
David Steurer
April 14, 2010
Abstract
We give subexponential time approximation algorithms for UNIQUE GAMES and the SMALLSET EXPAN
SION. Specifically, for some absolute constant c, we give:
1. An exp(kn
)time algorithm that, given as input a kalphabet 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 nvertex 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
