The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Christopher Umans - One of the best experts on this subject based on the ideXlab platform.
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On the Complexity of Succinct Zero-Sum Games
computational complexity, 2008Co-Authors: Lance Fortnow, Russell Impagliazzo, Christopher UmansAbstract:We study the complexity of solving succinct zero-sum games, i.e., the games whose payoff matrix M is given implicitly by a Boolean circuit C such that M ( i , j ) = C ( i , j ). We complement the known EXP -hardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum game to within an additive error is complete for the class promise - $$S^{p}_{2}$$ , the “promise” version of $$S^{p}_{2}$$ . To the best of our knowledge, it is the first natural problem shown complete for this class. (2) We describe a ZPP ^ NP algorithm for constructing approximately optimal strategies, and hence for approximating the value, of a given succinct zero-sum game. As a corollary, we obtain, in a uniform fashion, several complexity-theoretic results, e.g., a ZPP ^ NP algorithm for learning circuits for SAT (Bshouty et al., JCSS , 1996) and a recent result by Cai ( JCSS , 2007) that $$S^{p}_{2} \subseteq$$ ZPP ^ NP . (3) We observe that approximating the value of a succinct zero-sum game to within a Multiplicative Factor is in PSPACE , and that it cannot be in promise - $$S^{p}_{2}$$ unless the polynomial-time hierarchy collapses. Thus, under a reasonable complexity-theoretic assumption, Multiplicative-Factor approximation of succinct zero-sum games is strictly harder than additive-error approximation.
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on the complexity of succinct zero sum games
Conference on Computational Complexity, 2005Co-Authors: Lance Fortnow, Russell Impagliazzo, Christopher UmansAbstract:We study the complexity of solving succinct zero-sum games, i.e., the games whose payoff matrix M is given implicitly by a Boolean circuit C such that M(i, j) = C(i, j). We complement the known EXP-hardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum game to within an additive Factor is complete for the class promise-S/sub 2//sup p/, the "promise" version of S/sub 2//sup p/. To the best of our knowledge, it is the first natural problem shown complete for this class. (2) We describe a ZPP/sup NP/ algorithm for constructing approximately optimal strategies, and hence for approximating the value, of a given succinct zero-sum game. As a corollary, we obtain, in a uniform fashion, several complexity-theoretic results, e.g., a ZPP/sup NP/ algorithm for learning circuits for SAT (Bshouty et al., 1996) and a recent result by Cai (2001) that S/sub 2//sup p/ /spl sube/ ZPP/sup NP/. (3) We observe that approximating the value of a succinct zero-sum game to within a Multiplicative Factor is in PSPACE, and that it cannot be in promise-S/sub 2//sup p/ unless the polynomial-time hierarchy collapses. Thus, under a reasonable complexity-theoretic assumption, Multiplicative Factor approximation of succinct zero-sum games is strictly harder than additive Factor approximation.
Mark Van Der Meijde - One of the best experts on this subject based on the ideXlab platform.
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On seismic ambient noise cross-correlation and surface-wave attenuation
Geophysical Journal International, 2019Co-Authors: Lapo Boschi, Fabrizio Magrini, Fabio Cammarano, Mark Van Der MeijdeAbstract:We derive a theoretical relationship between the cross correlation of ambient Rayleigh waves (seismic ambient noise) and the attenuation parameter α associated with Rayleigh-wave propagation. In particular, we derive a mathematical expression for the Multiplicative Factor relating normalized cross correlation to the Rayleigh-wave Green’s function. Based on this expression, we formulate an inverse problem to determine α from cross correlations of recorded ambient signal. We conduct a preliminary application of our algorithm to a relatively small instrument array, conveniently deployed on an island. In our setup, the mentioned Multiplicative Factor has values of about 2.5–3, which, if neglected, could result in a significant underestimate of α. We find that our inferred values of α are reasonable, in comparison with independently obtained estimates found in the literature. Allowing α to vary with respect to frequency results in a reduction of misfit between observed and predicted cross correlations.
Lance Fortnow - One of the best experts on this subject based on the ideXlab platform.
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On the Complexity of Succinct Zero-Sum Games
computational complexity, 2008Co-Authors: Lance Fortnow, Russell Impagliazzo, Christopher UmansAbstract:We study the complexity of solving succinct zero-sum games, i.e., the games whose payoff matrix M is given implicitly by a Boolean circuit C such that M ( i , j ) = C ( i , j ). We complement the known EXP -hardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum game to within an additive error is complete for the class promise - $$S^{p}_{2}$$ , the “promise” version of $$S^{p}_{2}$$ . To the best of our knowledge, it is the first natural problem shown complete for this class. (2) We describe a ZPP ^ NP algorithm for constructing approximately optimal strategies, and hence for approximating the value, of a given succinct zero-sum game. As a corollary, we obtain, in a uniform fashion, several complexity-theoretic results, e.g., a ZPP ^ NP algorithm for learning circuits for SAT (Bshouty et al., JCSS , 1996) and a recent result by Cai ( JCSS , 2007) that $$S^{p}_{2} \subseteq$$ ZPP ^ NP . (3) We observe that approximating the value of a succinct zero-sum game to within a Multiplicative Factor is in PSPACE , and that it cannot be in promise - $$S^{p}_{2}$$ unless the polynomial-time hierarchy collapses. Thus, under a reasonable complexity-theoretic assumption, Multiplicative-Factor approximation of succinct zero-sum games is strictly harder than additive-error approximation.
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on the complexity of succinct zero sum games
Conference on Computational Complexity, 2005Co-Authors: Lance Fortnow, Russell Impagliazzo, Christopher UmansAbstract:We study the complexity of solving succinct zero-sum games, i.e., the games whose payoff matrix M is given implicitly by a Boolean circuit C such that M(i, j) = C(i, j). We complement the known EXP-hardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum game to within an additive Factor is complete for the class promise-S/sub 2//sup p/, the "promise" version of S/sub 2//sup p/. To the best of our knowledge, it is the first natural problem shown complete for this class. (2) We describe a ZPP/sup NP/ algorithm for constructing approximately optimal strategies, and hence for approximating the value, of a given succinct zero-sum game. As a corollary, we obtain, in a uniform fashion, several complexity-theoretic results, e.g., a ZPP/sup NP/ algorithm for learning circuits for SAT (Bshouty et al., 1996) and a recent result by Cai (2001) that S/sub 2//sup p/ /spl sube/ ZPP/sup NP/. (3) We observe that approximating the value of a succinct zero-sum game to within a Multiplicative Factor is in PSPACE, and that it cannot be in promise-S/sub 2//sup p/ unless the polynomial-time hierarchy collapses. Thus, under a reasonable complexity-theoretic assumption, Multiplicative Factor approximation of succinct zero-sum games is strictly harder than additive Factor approximation.
Stephane Rovedakis - One of the best experts on this subject based on the ideXlab platform.
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fast self stabilizing minimum spanning tree construction using compact nearest common ancestor labeling scheme
arXiv: Distributed Parallel and Cluster Computing, 2013Co-Authors: Lelia Blin, Shlomi Dolev, Maria Potopbutucaru, Stephane RovedakisAbstract:We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of previously known self-stabilizing asynchronous MST algorithms by a Multiplicative Factor $\Theta(n)$, to the price of increasing the best known space complexity by a Factor $O(\log n)$. The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only $O(\log^2n)$ bits.
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fast self stabilizing minimum spanning tree construction using compact nearest common ancestor labeling scheme
International Symposium on Distributed Computing, 2010Co-Authors: Lelia Blin, Shlomi Dolev, Maria Potopbutucaru, Stephane RovedakisAbstract:We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is O(log2 n) bits and it converges in O(n2) rounds. Thus, this algorithm improves the convergence time of all previously known self-stabilizing asynchronous MST algorithms by a Multiplicative Factor Θ(n), to the price of increasing the best known space complexity by a Factor O(log n). The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only O(log2 n) bits.
Lapo Boschi - One of the best experts on this subject based on the ideXlab platform.
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On seismic ambient noise cross-correlation and surface-wave attenuation
Geophysical Journal International, 2019Co-Authors: Lapo Boschi, Fabrizio Magrini, Fabio Cammarano, Mark Van Der MeijdeAbstract:We derive a theoretical relationship between the cross correlation of ambient Rayleigh waves (seismic ambient noise) and the attenuation parameter α associated with Rayleigh-wave propagation. In particular, we derive a mathematical expression for the Multiplicative Factor relating normalized cross correlation to the Rayleigh-wave Green’s function. Based on this expression, we formulate an inverse problem to determine α from cross correlations of recorded ambient signal. We conduct a preliminary application of our algorithm to a relatively small instrument array, conveniently deployed on an island. In our setup, the mentioned Multiplicative Factor has values of about 2.5–3, which, if neglected, could result in a significant underestimate of α. We find that our inferred values of α are reasonable, in comparison with independently obtained estimates found in the literature. Allowing α to vary with respect to frequency results in a reduction of misfit between observed and predicted cross correlations.
