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Exact Sampling from Perfect Matchings of Dense Regular Bipartite Graphs

2005
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Algorithmica
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We present the first algorithm for generating random variates exactly uniformly from the set of perfect matchings of a bipartite graph with a polynomial expected running time over a nontrivial set of graphs. Previous Markov chain results obtain approximately uniform variates for arbitrary graphs in polynomial time, but their general running time is (n 10 (ln n) 2 ). Other algorithms (such as Kasteleyn's O(n 3 ) algorithm for planar graphs) concentrated on restricted versions of the problem. Our

doi:10.1007/s00453-005-1175-9
fatcat:n5ynlfcahvchtd3dypuxrjwk4i