Computing a Many-to-Many Matching with Demands and Capacities between Two Sets Using the Hungarian Algorithm

Abstract

A many-to-many matching (MM) between two sets matches each element of one set to at least one element of the other set. A general case of the MM is the many-to-many matching with demands and capacities (MMDC) satisfying given lower and upper bounds on the number of elements matched to each element. In this article, we give a polynomial-time algorithm for finding a minimum-cost MMDC between two sets using the well-known Hungarian algorithm.