TY - JOUR
T1 - Computing the partition function for perfect matchings in a hypergraph
AU - Barvinok, Alexander
AU - Samorodnitsky, Alex
PY - 2011/11
Y1 - 2011/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80055081570&partnerID=8YFLogxK
U2 - 10.1017/S0963548311000435
DO - 10.1017/S0963548311000435
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AN - SCOPUS:80055081570
SN - 0963-5483
VL - 20
SP - 815
EP - 835
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 6
ER -