Unique games on expanding constraint graphs are easy: extended abstract

Authors:
Sanjeev Arora;Subhash A. Khot;Alexandra Kolla;David Steurer;Madhur Tulsiani;Nisheeth K. Vishnoi
Affiliations:
Princeton University, Princeton, NJ, USA;Courant Institue of Mathematical Sciences, New York University, New York, NY, USA;University of California, Berkeley, Berkeley, CA, USA;Princeton University, Princeton, NJ, USA;University of California, Berkeley, Berkeley, CA, USA;IBM India Research Lab, Delhi, India
Venue:
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Year:
2008

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Abstract

We present an efficient algorithm to find a good solution to the Unique Games problem when the constraint graph is an expander. We introduce a new analysis of the standard SDP in this case that involves correlations among distant vertices. It also leads to a parallel repetition theorem for unique games when the graph is an expander.