Results 1  10
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199
Efficient Deterministic Approximate Counting for LowDegree Polynomial Threshold Functions
"... ABSTRACT We give a deterministic algorithm for approximately counting satisfying assignments of a degreed polynomial threshold function (PTF). Given a degreed input polynomial p(x) over R n and a parameter > 0, our algorithm approximates (Since it is NPhard to determine whether the above prob ..."
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ABSTRACT We give a deterministic algorithm for approximately counting satisfying assignments of a degreed polynomial threshold function (PTF). Given a degreed input polynomial p(x) over R n and a parameter > 0, our algorithm approximates (Since it is NPhard to determine whether the above
Approximate Counts and Quantiles over Sliding Windows
 Proc. of ACM PODS Symp
, 2004
"... We consider the problem of maintaining approximate counts and quantiles over fixed and variablesize sliding windows in limited space. For quantiles, we present deterministic algorithms whose space requirements are O ( 1! log 1! logN) and O( ..."
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Cited by 97 (1 self)
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We consider the problem of maintaining approximate counts and quantiles over fixed and variablesize sliding windows in limited space. For quantiles, we present deterministic algorithms whose space requirements are O ( 1! log 1! logN) and O(
Deterministic Approximate Counting of Depth2 Circuits
, 1993
"... We describe deterministic algorithms which for a given depth2 circuit F approximate the probability that on a random input F outputs a specific value α. Our approach gives an algorithm which for a given GF[2] multivariate polynomial p and given ε > 0 approximates the number ..."
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Cited by 22 (6 self)
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We describe deterministic algorithms which for a given depth2 circuit F approximate the probability that on a random input F outputs a specific value α. Our approach gives an algorithm which for a given GF[2] multivariate polynomial p and given ε > 0 approximates
A deterministic polynomialtime approximation scheme for counting knapsack solutions
, 1008
"... Abstract. Given n elements with nonnegative integer weights w1,...,wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given capacity. We give a deterministic algorithm that estimates ..."
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Cited by 6 (0 self)
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Abstract. Given n elements with nonnegative integer weights w1,...,wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given capacity. We give a deterministic algorithm that estimates
Deterministic approximate counting for degree2 polynomial threshold functions. manuscript
, 2013
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Deterministic approximate counting for juntas of degree2 polynomial threshold functions. manuscript
, 2013
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A note on deterministic approximate counting for kDNF
 In: APPROXRANDOM
, 2004
"... We describe a deterministic algorithm that, for constant k, given a kDNF or kCNF formula ϕ and a parameter ε, runs in time linear in the size of ϕ and polynomial in 1/ε and returns an estimate of the fraction of satisfying assignments for ϕ up to an additive error ε. For kDNF, a multiplicative ap ..."
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Cited by 6 (0 self)
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We describe a deterministic algorithm that, for constant k, given a kDNF or kCNF formula ϕ and a parameter ε, runs in time linear in the size of ϕ and polynomial in 1/ε and returns an estimate of the fraction of satisfying assignments for ϕ up to an additive error ε. For kDNF, a multiplicative
Complexity Measures and Decision Tree Complexity: A Survey
 Theoretical Computer Science
, 2000
"... We discuss several complexity measures for Boolean functions: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. We survey the relations and biggest gaps known between these measures, and show how they give bounds for the decision tr ..."
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Cited by 197 (17 self)
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We discuss several complexity measures for Boolean functions: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. We survey the relations and biggest gaps known between these measures, and show how they give bounds for the decision
Pseudorandomness for approximate counting and sampling
 In Proceedings of the 20th IEEE Conference on Computational Complexity
, 2005
"... We study computational procedures that use both randomness and nondeterminism. Examples are ArthurMerlin games and approximate counting and sampling of NPwitnesses. The goal of this paper is to derandomize such procedures under the weakest possible assumptions. Our main technical contribution allow ..."
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Cited by 22 (5 self)
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to construct these primitives using an assumption that is no stronger than that used to derandomize AM. As a consequence, under this assumption, there are deterministic polynomial time algorithms that use nonadaptive NPqueries and perform the following tasks: • approximate counting of NPwitnesses: given a
Counting independent sets up to the tree threshold
 In STOC ’06: Proceedings of the thirtyeighth annual ACM symposium on Theory of computing
, 2006
"... Consider the problem of approximately counting weighted independent sets of a graph G with activity λ, i.e., where the weight of an independent set I is λ I . We present a novel analysis yielding a deterministic approximation scheme which runs in polynomial time for any graph of maximum degree Δ ..."
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Cited by 89 (1 self)
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Consider the problem of approximately counting weighted independent sets of a graph G with activity λ, i.e., where the weight of an independent set I is λ I . We present a novel analysis yielding a deterministic approximation scheme which runs in polynomial time for any graph of maximum degree Δ
Results 1  10
of
199