SIAM Journal on Computing
A Monte-Carlo algorithm for estimating the permanent
SIAM Journal on Computing
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Random Structures & Algorithms
Approximating the permanent via importance sampling with application to the dimer covering problem
Journal of Computational Physics
Clifford algebras and approximating the permanent
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Random sampling for the monomer-dimer model on a lattice
Random sampling for the monomer-dimer model on a lattice
Approximately Counting Embeddings into Random Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Multivariable goodness tests and approximation of the residues of quadratic forms
Automation and Remote Control
Counting perfect matchings as fast as Ryser
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A randomized approximation algorithm for parameterized 3-D matching counting problem
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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We present two new methods for counting all matchings in a graph. Both methods are alternatives to methods based on the Markov Chains and both are unbiased. The first one is a generalization of a Godman-Godsil estimator. We show that it works in time O(1.0878n驴-2) for general graphs. For dense graphs (every vertex is connected with at least (1/2 +驴)n other vertices) it works in time O(n4+(6 ln 6)/驴驴-2), where n is the number of vertices of a given graph and 0