A note on unique games

Authors:
Adi Avidor;Ricky Rosen
Affiliations:
Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel;Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
Venue:
Information Processing Letters
Year:
2006

Citing 12
Cited 0

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Abstract

We give a tighter analysis of the algorithm of Khot [S. Khot, On the power of unique 2-prover 1-round games, in: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, Montreal, Quebec, Canada, 2002, pp. 767-775] which shows that given a unique 2-prover-1-round game with value 1 - ε, one can find in polynomial time an assignment to the game with an expected weight of 1 - O(k6/5ε1/5 (log 1/εk)2/5), where k is the size of the answer domain. This shows that if the Unique Games Conjecture is true then the domain size k, must be at least Ω((ε1/6 log1/3(1/ε)) -1), which is an improvement over the previous Ω((ε1/10 log1/4(1/ε))-1) bound.