# Subexponential Algorithms for Unique Games and Related Problems

@article{Arora2010SubexponentialAF,
title={Subexponential Algorithms for Unique Games and Related Problems},
author={Sanjeev Arora and Boaz Barak and David Steurer},
journal={2010 IEEE 51st Annual Symposium on Foundations of Computer Science},
year={2010},
pages={563-572}
}
• Published 2010
• Computer Science, Mathematics
• 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
We give a sub exponential time approximation algorithm for the \textsc{Unique Games} problem. The algorithms run in time that is exponential in an arbitrarily small polynomial of the input size, $n^{\epsilon}$. The approximation guarantee depends on~$\epsilon$, but not on the alphabet size or the number of variables. We also obtain a sub exponential algorithms with improved approximations for \textsc{Small-Set Expansion} and \textsc{Multicut}. For \textsc{Max Cut}, \textsc{Sparsest Cut}, and… Expand
218 Citations

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Lasserre Hierarchy, Higher Eigenvalues, and Approximation Schemes for Quadratic Integer Programming with PSD Objectives
• Computer Science, Mathematics
• Electron. Colloquium Comput. Complex.
• 2011
An approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints, and an algorithm for independent sets in graphs that performs well when the Laplacian does not have too many eigenvalues bigger than $1+o(1)$. Expand
Playing Random and Expanding Unique Games
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In this work, we present a spectral algorithm that finds good assignments for instances of Unique Games when the underlying graph has some significant expansion and the constraints are arbitraryExpand
Optimal algorithms and inapproximability results for every CSP?
A generic conversion from SDP integrality gaps to UGC hardness results for every CSP is shown, which achieves at least as good an approximation ratio as the best known algorithms for several problems like MaxCut, Max2Sat, MaxDiCut and Unique Games. Expand
Which Problems Have Strongly Exponential Complexity
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For several NP-complete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of sub-exponential algorithms for theseExpand