Approximation Algorithms for Maximization of $k$-Submodular Function Under a Matroid Constraint

Abstract

In this paper, we design a deterministic 1/3-approximation algorithm for the problem of maximizing non-monotone $k$ -submodular function under a matroid constraint. In order to reduce the complexity of this algorithm, we also present a randomized 1/3-approximation algorithm with the probability of $1-\varepsilon$ , where $\varepsilon$ is the probability of algorithm failure. Moreover, we design a streaming algorithm for both monotone and non-monotone objective $k$ -submodular functions.