Given a natural number k≥2, we consider the k-submodular cover problem (k-SC). The objective is to find a minimum cost subset of a ground set X subject to the value of a k-submodular utility function being at least a certain predetermined value τ. For this problem, we design a bicriteria algorithm with a cost at most O(1/ϵ) times the optimal value, while the utility is at least (1−ϵ)τ/r, where r depends on the monotonicity of g.
@article{arxiv.2312.03593,
title = {Streaming Algorithms for the $k$-Submodular Cover Problem},
author = {Wenqi Wang and Gregory Gutin and Yaping Mao and Donglei Du and Xiaoyan Zhang},
journal= {arXiv preprint arXiv:2312.03593},
year = {2023}
}