Abstract
In this paper, we improve a result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a (1 − ε)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignment satisfying at least a 1 − C ε/h G fraction of all constraints if ε < c λ G where h G is the edge expansion of G, λ G is the second smallest eigenvalue of the Laplacian of G, and C and c are some absolute constants.
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Makarychev, K., Makarychev, Y. (2011). How to Play Unique Games on Expanders. In: Jansen, K., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2010. Lecture Notes in Computer Science, vol 6534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18318-8_17
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DOI: https://doi.org/10.1007/978-3-642-18318-8_17
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