Spectral Algorithms for Unique Games

Details Spectral Algorithms for Unique Games Spectral Algorithms for Unique Games

2011-02-11

arxiv.org/abs/1102.2300v1

Computer Science

Computational Complexity

Scientific paper

We give a new algorithm for Unique Games which is based on purely {\em spectral} techniques, in contrast to previous work in the area, which relies heavily on semidefinite programming (SDP). Given a highly satisfiable instance of Unique Games, our algorithm is able to recover a good assignment. The approximation guarantee depends only on the completeness of the game, and not on the alphabet size, while the running time depends on spectral properties of the {\em Label-Extended} graph associated with the instance of Unique Games. We further show that on input the integrality gap instance of Khot and Vishnoi, our algorithm runs in quasi-polynomial time and decides that the instance if highly unsatisfiable. Notably, when run on this instance, the standard SDP relaxation of Unique Games {\em fails}. As a special case, we also re-derive a polynomial time algorithm for Unique Games on expander constraint graphs. The main ingredient of our algorithm is a technique to effectively use the full spectrum of the underlying graph instead of just the second eigenvalue, which is of independent interest. The question of how to take advantage of the full spectrum of a graph in the design of algorithms has been often studied, but no significant progress was made prior to this work.

Affiliated with

Also associated with

No associations

Rating

Spectral Algorithms for Unique Games does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spectral Algorithms for Unique Games, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral Algorithms for Unique Games will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-632330