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Results 1 - 10
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199
Efficient Deterministic Approximate Counting for Low-Degree Polynomial Threshold Functions
"... ABSTRACT We give a deterministic algorithm for approximately counting satisfying assignments of a degree-d polynomial threshold function (PTF). Given a degree-d input polynomial p(x) over R n and a parameter > 0, our algorithm approximates (Since it is NP-hard to determine whether the above prob ..."
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ABSTRACT We give a deterministic algorithm for approximately counting satisfying assignments of a degree-d polynomial threshold function (PTF). Given a degree-d input polynomial p(x) over R n and a parameter > 0, our algorithm approximates (Since it is NP-hard 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 variable-size 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 variable-size 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 Depth-2 Circuits
, 1993
"... We describe deterministic algorithms which for a given depth-2 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 depth-2 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 polynomial-time 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 degree-2 polynomial threshold functions. manuscript
, 2013
"... ar ..."
Deterministic approximate counting for juntas of degree-2 polynomial threshold functions. manuscript
, 2013
"... ar ..."
A note on deterministic approximate counting for k-DNF
- In: APPROX-RANDOM
, 2004
"... We describe a deterministic algorithm that, for constant k, given a k-DNF or k-CNF 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 k-DNF, 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 k-DNF or k-CNF 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 k-DNF, 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 Arthur-Merlin 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 non-adaptive NP-queries and perform the following tasks: • approximate counting of NP-witnesses: given a
Counting independent sets up to the tree threshold
- In STOC ’06: Proceedings of the thirty-eighth 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 de-gree 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 de-gree Δ
Results 1 - 10
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199
