An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Harold N. Gabow · Journal of the ACM · 1976
A matching on a graph is a set 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 a maximum matching. The computation time is proportional to V 3 , where V is the number of vertices; previous implementations of Edmonds' algorithm have computation time proportional to V 4 . The implementation is based on a system of labels that encodes the structure of alternating paths.