We consider Karp-Sipser, a well known matching heuristic in the context of data reduction for the maximum cardinality matching problem. We describe an efficient implementation as well as modifications to reduce its time complexity in worst case instances, both in theory and in practical cases. We compare experimentally against its widely used simpler variant and show cases for which the full algorithm yields better performance.
We investigate efficient randomized methods for approximating the number of perfect matchings in bipartite graphs and general graphs. Our approach is based on assigning probabilities to edges.
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.
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