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Computing the Partition Function for Perfect Matchings in a Hypergraph

Published online by Cambridge University Press:  17 October 2011

ALEXANDER BARVINOK  and
ALEX SAMORODNITSKY
ALEXANDER BARVINOK
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA (e-mail: [email protected])
ALEX SAMORODNITSKY
Affiliation:
Department of Computer Science, Hebrew University of Jerusalem, Givat Ram Campus, 91904, Israel (e-mail: [email protected])
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Abstract

Given non-negative weights wS on the k-subsets S of a km-element set V, we consider the sum of the products wS1 ⋅⋅⋅ wSm over all partitions V = S1 ∪ ⋅⋅⋅ ∪Sm into pairwise disjoint k-subsets Si. When the weights wS are positive and within a constant factor of each other, fixed in advance, we present a simple polynomial-time algorithm to approximate the sum within a polynomial in m factor. In the process, we obtain higher-dimensional versions of the van der Waerden and Bregman–Minc bounds for permanents. We also discuss applications to counting of perfect and nearly perfect matchings in hypergraphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 6 , November 2011 , pp. 815 - 835
Copyright
Copyright © Cambridge University Press 2011

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