$k$-Submodular Maximization with a Knapsack Constraint and $p$ Matroid Constraints

Abstract

A $k$ -submodular function is a generalization of a submodular function, its definition domain is extended from the collection of single subsets to the collection of $k$ disjoint subsets. The $k$ -submodular maximization problem has a wide range of applications. In this paper, we propose a nested greedy and local search algorithm for the problem of maximizing a monotone $k$ -submodular function subject to a knapsack constraint and $p$ matroid constraints.