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Published in:
2006 | OriginalPaper | Chapter
Fractional Matching Via Balls-and-Bins
Authors : Rajeev Motwani, Rina Panigrahy, Ying Xu
Published in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Publisher: Springer Berlin Heidelberg
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We relate the problem of finding structures related to perfect matchings in bipartite graphs to a stochastic process similar to throwing balls into bins. We view each node on the left of a bipartite graph as having balls that it can throw into nodes on the right (bins) to which it is adjacent. We show that several simple algorithms based on throwing balls into bins deliver a near-perfect fractional matching, where a perfect fractional matching is a weighted subgraph on all nodes with nonnegative weights on edges so that the total weight incident at each node is 1.