# 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} }

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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#### References

SHOWING 1-10 OF 21 REFERENCES

An O (N2.5) algorithm for maximum matching in general graphs

- Computer Science, Mathematics
- 16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
- 1975

An n5/2 Algorithm for Maximum Matchings in Bipartite Graphs

- Mathematics, Computer Science
- SIAM J. Comput.
- 1973

Combinatorial Optimization Theory

- Combinatorial Optimization Theory
- 1976

1.. itA o( IV I· IE I) Algorithm for Maximum Matching of Graphs

- Computing
- 1974

An n 2 . 5 Algorithm for Maximum Matching in Bipartite Graphs

- SIAM J. on Compo
- 1973

Paths, Trees apd FlowersMaximum Matching and Polyhedron with 0,1 Vertices

- Canadian J. Journal of Research of the National Bureau of Standards
- 1965

0 (boundary condition) If high=low then Path:=high and go to step(~ 0.1 (initialization) v: =high

- 0 (boundary condition) If high=low then Path:=high and go to step(~ 0.1 (initialization) v: =high

Create a new blossom (a set) B. Let B consist of all vertices that were marked "left" or "right" during the present call. peakL{B):= Wt, peakR{B)~= wa

- Create a new blossom (a set) B. Let B consist of all vertices that were marked "left" or "right" during the present call. peakL{B):= Wt, peakR{B)~= wa