An O(v|v| c |E|) algoithm for finding maximum matching in general graphs

@article{Micali1980AnOC,
  title={An O(v|v| c |E|) algoithm for finding maximum matching in general graphs},
  author={S. Micali and V. Vazirani},
  journal={21st Annual Symposium on Foundations of Computer Science (sfcs 1980)},
  year={1980},
  pages={17-27}
}
  • S. Micali, V. Vazirani
  • Published 1980
  • Mathematics, Computer Science
  • 21st Annual Symposium on Foundations of Computer Science (sfcs 1980)
In this paper we present an 0(√|V|¿|E|) algorithm for finding a maximum matching in general graphs. This algorithm works in 'phases'. In each phase a maximal set of disjoint minimum length augmenting paths is found, and the existing matching is increased along these paths. Our contribution consists in devising a special way of handling blossoms, which enables an O(|E|) implementation of a phase. In each phase, the algorithm grows Breadth First Search trees at all unmatched vertices. When it… Expand
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0 (boundary condition) If high=low then Path:=high and go to step(~ 0.1 (initialization) v: =high
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