Maximum Matching in a Partially Matched Bipartite Graph and Its Applications

Abstract

This paper discusses an approach to solve the maximum matching problem in Bipartite graph (B-graph) where the graph is partially matched and the existing matches cannot be changed. It uses the approach of choosing vertices for matching based on the run-time weight calculation. Vertex with highest weight is given preference for matching. Weights are assigned to vertices based on its number of matched, pass-through and un-matched edges. Matching is done by choosing vertices with highest weight from both disjoint set of vertices and continuing to form an Alternative path (A-path). This approach leads to finding and traversing through maximum number of A-paths (with no shared vertex) and making maximum matching in each of those A-paths. This condition will result in a B-graph which will have the maximum possible matching. 2N-Soft-fail Sector Redundancy for Access Points is one of the applications explained in this paper.