An efficient algorithm for minimizing M-convex functions under a color-induced budget constraint

Abstract

In this paper, we present an efficient algorithm for minimizing an M♮-convex function under a color-induced budget constraint. The algorithm extends the algorithms by Gabow and Tarjan for finding a minimum-weight base of a matroid and by Gottschalk et al. for minimizing a separable discrete convex function on a polymatroid under a color-induced budget constraint. It can also be recognized as an extension of a greedy algorithm for unconstrained M♮-convex function minimization by Murota and Shioura.