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

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2 Author(s)

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 detects the presence of a blossom, it does not 'shrink' the blossom immediately. Instead, it delays the shrinking in such a way that the first augmenting path found is of minimum length. Furthermore, it achieves the effect of shrinking a blossom by a special labeling procedure which enables it to find an augmenting path through a blossom quickly.

Published in:

Foundations of Computer Science, 1980., 21st Annual Symposium on

Date of Conference:

13-15 Oct. 1980