Effective Heuristics for Matchings in Hypergraphs

Abstract

The problem of finding a maximum cardinality matching in a d-partite, d-uniform hypergraph is an important problem in combinatorial optimization and has been theoretically analyzed. We first generalize some graph matching heuristics for this problem. We then propose a novel heuristic based on tensor scaling to extend the matching via judicious hyperedge selections. Experiments on random, synthetic and real-life hypergraphs show that this new heuristic is highly practical and superior to the others on finding a matching with large cardinality.

Distributed Algorithms for Matching in Hypergraphs

“…However, the ratio is smaller when compared to a maximal matching, which is explained by the deterioration of the quality of greedy maximal matching as n and d grow. Dufosse et al [23] confirm that the approximation quality of a greedy maximal matching on random graphs that contain a perfect matching degrades as a function of n and d. The performance of the algorithms decreases as d grows, which is theoretically expected since their approximations ratio are both proportional to d. The number of rounds for Iterated-Sampling grows slowly with n, which is consistent with O(log n) bound. Recall that the number of rounds for the other two algorithms is constant and equal to 3.…”