Sensitivity Analysis of the Bipartite Weighted Matching Problem

Summary

Let G be an undirected bipartite graph where a weight is assigned to every edge. A maximum weighted matching can be computed on G. We define slightly changed problems of the original matching problem. One type of problem is to delete a vertex, a pair of vertices or an edge from G. A second type of problem can be constructed if a vertex or a pair of vertices is doubled by making an identical copy. A third type of problem is the replacement of a vertex by a copy of another vertex. All these problems build up some kind of sensitivity analysis of the original problem and are of special interest for example in man power scheduling. We can show that all these problems can be solved simultaneously by finding the shortest path between all pairs of vertices in a graph G′ which can easily be constructed