Characterization and algorithm for bivariate multi-unit assignment valuations

Abstract

AbstractA multi-unit assignment valuation is a function represented by a weighted bipartite graph. In this paper, we provide a characterization of such a function in terms of maximizer sets of perturbed functions. We then present an algorithm that checks whether a given bivariate function is a multi-unit assignment valuation, and if the answer is “yes,” computes a weighted bipartite graph representing the function.