How to Play Unique Games on Expanders

Konstantin Makarychev; Yury Makarychev

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arXiv · 0903.0367

How to Play Unique Games on Expanders

Konstantin Makarychev·Yury Makarychev

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Abstract

In this note we improve a recent result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a $(1-\varepsilon)$-satisfiable instance of Unique Games with the constraint graph $G$, our algorithm finds an assignment satisfying at least a $1- C \varepsilon/h_G$ fraction of all constraints if $\varepsilon < c λ_G$ 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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BibTeX RIS

Konstantin Makarychev, Yury Makarychev. 2009-03-02. How to Play Unique Games on Expanders. https://arxiv.org/abs/0903.0367

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