Randomly Supported Independence and Resistance
SIAM Journal on Computing
A new point of NP-hardness for unique games
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Multireference alignment using semidefinite programming
Proceedings of the 5th conference on Innovations in theoretical computer science
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We present a new algorithm for Unique Games which is based on purely {\em spectral} techniques, in contrast to previous work in the area, which relies heavily on semidefinite programming (SDP). Given a highly satisfiable instance of Unique Games, our algorithm is able to recover a good assignment. The approximation guarantee depends only on the completeness of the game, and not on the alphabet size, while the running time depends on spectral properties of the {\em Label-Extended} graph associated with the instance of Unique Games. In particular, we show how our techniques imply a quasi-polynomial time algorithm that decides satisfiability of a game on the Khot-Vishnoi\cite{KV} integrality gap instance. Notably, when run on that instance, the standard SDP relaxation of Unique Games {\em fails}. As a special case, we also show how to re-derive a polynomial time algorithm for Unique Games on expander constraint graphs (similar to \cite{AKKTSV}) and a sub-exponential time algorithm for Unique Games on the Hypercube.