FINDING A COMPLETE MATCHING WITH THE MAXIMUM PRODUCT ON WEIGHTED BIPARTITE GRAPHS

Abstract

The traditional bipartite weighted matching problem is to maximize the largest possible sum of weights. In this paper, we define a bipartite matching problem which maximizes the largest possible product of weights and develop an algorithm to solve it. Although this problem corresponds to a non-linear program, we show this problem can be easily solved by modifying the Hungarian method. Finally, we present an application of this problem.