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667,722
Approximate counting, uniform generation and rapidly mixing markov chains
 Inf. Comput
, 1989
"... The paper studies effective approximate solutions to combinatorial counting and uniform generation problems. Using a technique based on the simulation of ergodic Markov chains, it is shown that, for selfreducible structures, almost uniform generation is possible in polynomial time provided only tha ..."
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Cited by 317 (11 self)
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The paper studies effective approximate solutions to combinatorial counting and uniform generation problems. Using a technique based on the simulation of ergodic Markov chains, it is shown that, for selfreducible structures, almost uniform generation is possible in polynomial time provided only
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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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
Approximate counting of regular hypergraphs
, 2013
"... In this paper we approximately count dregular kuniform hypergraphs on n vertices, provided k is fixed and d = d(n) = o(n κ), where κ = κ(k) = 1 for all k ≥ 4, while κ(3) = 1 2. In doing so, we extend to hypergraphs a switching technique of McKay and Wormald. ..."
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Cited by 4 (2 self)
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In this paper we approximately count dregular kuniform hypergraphs on n vertices, provided k is fixed and d = d(n) = o(n κ), where κ = κ(k) = 1 for all k ≥ 4, while κ(3) = 1 2. In doing so, we extend to hypergraphs a switching technique of McKay and Wormald.
Approximate counting in bounded arithmetic
, 2007
"... We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(P V)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in P V1 + ..."
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Cited by 2 (0 self)
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We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(P V)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in P V1
Fragments of Approximate Counting
, 2012
"... We study the longstanding open problem of giving ∀Σ b 1 separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeˇrábek’s theories for approximate counting and their subtheories. ..."
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Cited by 1 (0 self)
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We study the longstanding open problem of giving ∀Σ b 1 separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeˇrábek’s theories for approximate counting and their subtheories
Flexible approximate counting
 In 15th International Database Engineering & Applications Symposium, IDEAS 2011
, 2011
"... Approximate counting [18] is useful for data stream and database summarization. It can help in many settings that allow only one pass over the data, want low memory usage, and can accept some relative error. Approximate counters use fewer bits; we focus on 8bits but our results are general. These s ..."
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Cited by 2 (0 self)
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Approximate counting [18] is useful for data stream and database summarization. It can help in many settings that allow only one pass over the data, want low memory usage, and can accept some relative error. Approximate counters use fewer bits; we focus on 8bits but our results are general
Approximate counting: A detailed analysis
 BIT
, 1985
"... Approximate counting is an algorithm proposed by R. Morris which makes it possible to keep approximate counts of large numbers in small counters. The algorithm is useful for gathering statistics of a large number of events as well as for applications related to data compression (Todd et al.). We pro ..."
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Cited by 49 (3 self)
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Approximate counting is an algorithm proposed by R. Morris which makes it possible to keep approximate counts of large numbers in small counters. The algorithm is useful for gathering statistics of a large number of events as well as for applications related to data compression (Todd et al.). We
Approximate counting by dynamic programming
 PROCEEDINGS OF THE 35TH ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2003
"... We give efficient algorithms to sample uniformly, and count approximately, solutions to the zeroone knapsack problem. The algorithm is based on using dynamic programming to provide a deterministic relative approximation. Then "dart throwing " techniques are used to give arbitrar ..."
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Cited by 27 (3 self)
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We give efficient algorithms to sample uniformly, and count approximately, solutions to the zeroone knapsack problem. The algorithm is based on using dynamic programming to provide a deterministic relative approximation. Then "dart throwing " techniques are used to give
Approximately Counting KNAPSACK Solutions
, 2006
"... In this lecture, we study the counting and sampling versions of the knapsack problem. This is a further example (as with Eucledian TSP in the last lecture) of the power of simple dynamic programming based approaches. It also highlights the intimate connection between approximate counting and random ..."
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In this lecture, we study the counting and sampling versions of the knapsack problem. This is a further example (as with Eucledian TSP in the last lecture) of the power of simple dynamic programming based approaches. It also highlights the intimate connection between approximate counting and random
Approximate counting and quantum computation
 Combinatorics, Probability and Computing
, 2006
"... Motivated by the result that an ‘approximate ’ evaluation #P have of the Jones polynomial of a braid at a 5 th root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP to the counting class GapP, we introduce a form of addi ..."
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Cited by 11 (1 self)
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Motivated by the result that an ‘approximate ’ evaluation #P have of the Jones polynomial of a braid at a 5 th root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP to the counting class GapP, we introduce a form
Results 1  10
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667,722