Derandomization for k-submodular maximization

TL;DR

This paper presents a deterministic, polynomial-time derandomized algorithm for maximizing monotone k-submodular functions, achieving the same approximation ratio as the best known randomized algorithms.

Contribution

It introduces a derandomization of the existing approximation algorithm for monotone k-submodular maximization, maintaining the approximation ratio.

Findings

The algorithm is deterministic and polynomial-time.

It achieves a k/(2k-1) approximation ratio.

It extends previous randomized approaches to a deterministic setting.

Abstract

Submodularity is one of the most important property of combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of $k$-submodular function is NP-hard, and approximation algorithms are studied. For monotone $k$-submodular function, [Iwata, Tanigawa, and Yoshida 2016] gave $k/(2k-1)$-approximation algorithm. In this paper, we give a deterministic algorithm by derandomizing that algorithm. Derandomization scheme is from [Buchbinder and Feldman 2016]. Our algorithm is $k/(2k-1)$-approximation and polynomial-time algorithm.