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تسجيل مستخدم جديدStreaming Hardness of Unique Games
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We study the problem of approximating the value of a Unique Game instance in the streaming model. A simple count of the number of constraints divided by $p$, the alphabet size of the Unique Game, gives a trivial $p$-approximation that can be computed in $O(log n)$ space. Meanwhile, with high probability, a sample of $tilde{O}(n)$ constraints suffices to estimate the optimal value to $(1+epsilon)$ accuracy. We prove that any single-pass streaming algorithm that achieves a $(p-epsilon)$-approximation requires $Omega_epsilon(sqrt{n})$ space. Our proof is via a reduction from lower bounds for a communication problem that is a $p$-ary variant of the Boolean Hidden Matching problem studied in the literature. Given the utility of Unique Games as a starting point for reduction to other optimization problems, our strong hardness for approximating Unique Games could lead to downemph{stream} hardness results for streaming approximability for other CSP-like problems.
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These are the lecture notes for the DIMACS Tutorial Limits of Approximation Algorithms: PCPs and Unique Games held at the DIMACS Center, CoRE Building, Rutgers University on 20-21 July, 2009. This tutorial was jointly sponsored by the DIMACS Special
Focus on Hardness of Approximation, the DIMACS Special Focus on Algorithmic Foundations of the Internet, and the Center for Computational Intractability with support from the National Security Agency and the National Science Foundation. The speakers at the tutorial were Matthew Andrews, Sanjeev Arora, Moses Charikar, Prahladh Harsha, Subhash Khot, Dana Moshkovitz and Lisa Zhang. The sribes were Ashkan Aazami, Dev Desai, Igor Gorodezky, Geetha Jagannathan, Alexander S. Kulikov, Darakhshan J. Mir, Alantha Newman, Aleksandar Nikolov, David Pritchard and Gwen Spencer.
We consider the complexity properties of modern puzzle games, Hexiom, Cut the Rope and Back to Bed. The complexity of games plays an important role in the type of experience they provide to players. Back to Bed is shown to be PSPACE-Hard and the firs
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