Some Matching Problems for Bipartite Graphs

Abstract

Certam apphcatlons require finding a perfect matching in a bipartite graph that satisfies some additional properties For one such type of restncUon the problem is proven to be NP-complete. If for a single subset of edges no more than r edges may be included m the matching then an O(ne) algorithm is given An efficient algorithm for finding all perfect matchmgs is presented It requires O(e) time per matching and a total of O(e) space This algorithm may be used to calculate the permanent of a matrix Finally, the algorithm ts generahzed to find all maximum matchmgs. © 1978, ACM. All rights reserved.