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533
Some results on averagecase hardness within the polynomial hierarchy
 In Proceedings of the 26th Conference on Foundations of Software Technology and Theoretical Computer Science
, 2006
"... Abstract. We prove several results about the averagecase complexity of problems in the Polynomial Hierarchy (PH). We give a connection among averagecase, worstcase, and nonuniform complexity of optimization problems. Specifically, we show that if P NP is hard in the worstcase then it is either ..."
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Cited by 1 (0 self)
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Abstract. We prove several results about the averagecase complexity of problems in the Polynomial Hierarchy (PH). We give a connection among averagecase, worstcase, and nonuniform complexity of optimization problems. Specifically, we show that if P NP is hard in the worstcase then it is either
WorstCase Running Times for AverageCase Algorithms
"... Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space, then t ..."
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Cited by 3 (0 self)
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Abstract—Under a standard hardness assumption we exactly characterize the worstcase running time of languages that are in average polynomialtime over all polynomialtime samplable distributions. More precisely we show that if exponential time is not infinitely often in subexponential space
WorstCase to AverageCase Reductions Revisited
"... A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomialtime samplable distribution (e.g., the uniform distribution) and a language in NTIME(f(n)) for some polynomial function f, such that the language is hard on the average with respect to this dis ..."
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Cited by 5 (1 self)
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standard notion of averagecase complexity, in which the distribution on the inputs with respect to which we measure the averagecase complexity of the language, is only samplable in superpolynomial time. The significance of this result stems from the fact that in this nonstandard setting, [GSTS05] did show a
On the Theory of Average Case Complexity
 Journal of Computer and System Sciences
, 1997
"... This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works [Levin 84, Gurevich 87, Venkatesan and Levin 88] have focused on the existence of complete problems. We widen the scope to other basic questions in computational complexity. ..."
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Cited by 121 (6 self)
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. Our results include: ffl the equivalence of search and decision problems in the context of average case complexity; ffl an initial analysis of the structure of distributionalNP (i.e. NP problems coupled with "simple distributions") under reductions which preserve average polynomial
New connections between derandomization, worstcase complexity and averagecase complexity
 Electronic Colloquium on Computational Complexity
, 2006
"... We show that a mild derandomization assumption together with the worstcase hardness of NP implies the averagecase hardness of a language in nondeterministic quasipolynomial time. Previously such connections were only known for high classes such as EXP and PSPACE. There has been a long line of re ..."
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Cited by 2 (1 self)
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We show that a mild derandomization assumption together with the worstcase hardness of NP implies the averagecase hardness of a language in nondeterministic quasipolynomial time. Previously such connections were only known for high classes such as EXP and PSPACE. There has been a long line
Sums of squares, moment matrices and optimization over polynomials
, 2008
"... We consider the problem of minimizing a polynomial over a semialgebraic set defined by polynomial equations and inequalities, which is NPhard in general. Hierarchies of semidefinite relaxations have been proposed in the literature, involving positive semidefinite moment matrices and the dual theory ..."
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Cited by 154 (9 self)
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We consider the problem of minimizing a polynomial over a semialgebraic set defined by polynomial equations and inequalities, which is NPhard in general. Hierarchies of semidefinite relaxations have been proposed in the literature, involving positive semidefinite moment matrices and the dual
The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations
, 1993
"... We prove the following about the Nearest Lattice Vector Problem (in any `p norm), the Nearest Codeword Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NPhard. 2. If for some ..."
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Cited by 170 (7 self)
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. If for some ffl ? 0 there exists a polynomialtime algorithm that approximates the optimum within a factor of 2 log 0:5\Gammaffl n , then every NP language can be decided in quasipolynomial deterministic time, i.e., NP ` DTIME(n poly(log n) ). Moreover, we show that result 2 also holds for the Shortest
On the hardness of satisfiability with bounded occurrences in the polynomialtime hierarchy
 THEORY OF COMPUTING
, 2007
"... In 1991, Papadimitriou and Yannakakis gave a reduction implying the NPhardness of approximating the problem 3SAT with bounded occurrences. Their reduction is based on expander graphs. We present an analogue of this result for the second level of the polynomialtime hierarchy based on superconcen ..."
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Cited by 2 (1 self)
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In 1991, Papadimitriou and Yannakakis gave a reduction implying the NPhardness of approximating the problem 3SAT with bounded occurrences. Their reduction is based on expander graphs. We present an analogue of this result for the second level of the polynomialtime hierarchy based
Combinatorial Auctions with Decreasing Marginal Utilities
, 2001
"... This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross s ..."
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Cited by 202 (25 self)
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it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.
Zero Knowledge and the Chromatic Number
 Journal of Computer and System Sciences
, 1996
"... We present a new technique, inspired by zeroknowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max3coloring and max3sat, showing that it is hard to approximate the chromatic number wi ..."
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Cited by 196 (6 self)
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within \Omega\Gamma N ffi ), for some ffi ? 0. We then apply our technique in conjunction with the probabilistically checkable proofs of Hastad, and show that it is hard to approximate the chromatic number to within\Omega\Gamma N 1\Gammaffl ) for any ffl ? 0, assuming NP 6` ZPP. Here, ZPP denotes
Results 1  10
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533