Expanding Graphs and the Average-case Analysis of Algorithms for Matchings and Related Problems

@article{Motwani1989ExpandingGA,
  title={Expanding Graphs and the Average-case Analysis of Algorithms for Matchings and Related Problems},
  author={Rajeev Motwani},
  journal={J. ACM},
  year={1989},
  volume={41},
  pages={1329-1356}
}
Hall's Theorem states that a bipartite graph has a perfect matching if and only if every set of vertices has an equal number of neighbours. Equivalently, it states that every non-maximum matching has an augmenting path if the graph is an expander with expansion 1. We use this insight to demonstrate that if a graph is an expander with expansion more than one than every non-maximum matching has a short augmenting path and, therefore, the bipartite matching algorithm performs much better on such… CONTINUE READING
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