How to Play Unique Games on Expanders
Konstantin Makarychev, Yury Makarychev

TL;DR
This paper presents an improved algorithm for solving the Unique Games problem on expander graphs, achieving better approximation guarantees under certain spectral and expansion conditions.
Contribution
It refines previous results by providing a more effective algorithm with improved approximation bounds for Unique Games on expanders.
Findings
Algorithm finds assignments satisfying a large fraction of constraints.
Performance depends on graph expansion and spectral gap.
Results improve upon recent bounds for Unique Games on expanders.
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 -satisfiable instance of Unique Games with the constraint graph , our algorithm finds an assignment satisfying at least a fraction of all constraints if where is the edge expansion of , is the second smallest eigenvalue of the Laplacian of , and and are some absolute constants.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Optimization and Search Problems
