Computing the partition function for perfect matchings in a hypergraph

Alexander Barvinok*, Alex Samorodnitsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageAmerican English
Pages (from-to)815-835
Number of pages21
JournalCombinatorics Probability and Computing
Volume20
Issue number6
DOIs
StatePublished - Nov 2011

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