Non-monotone k-Submodular Function Maximization with Individual Size Constraints

Abstract

In the problem of maximizing non-monotone k-submodular function f under individual size constraints, the goal is to maximize the value of k disjoint subsets with size upper bounds B1, B2, …, Bk, respectively. This problem generalized both submodular maximization and k-submodular maximization problem with total size constraint. In this paper, we propose two results about this kind of problem. One is a 1Bm+4 -approximation algorithm, where Bm= max { B1, B2, …, Bk}. The other is a bi-criteria algorithm with approximation ratio 14, where each subset is allowed to exceed the size constraint by up to Bm, and in the worst case, only one subset will exceed Bm.