An efficient implementation of Edmonds'' maximum matching algorithm.
Harold N. Gabow · 1972
A matching in a graph is a collection of edges, no two of which share a vertex. A maximum matching contains the greatest number of edges possible. This paper presents an efficient implementation of Edmonds'' algorithm for finding maximum matchings. The computation time is proportional to $V^3$, where V is the number of vertices; previous algorithms have computation time proportional to $V^4$. The implementation avoids Edmonds'' blossom reduction by using pointers to encode the structure of alternating paths.