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arXiv · 2312.03593

Streaming Algorithms for the $k$-Submodular Cover Problem

Wenqi Wang·Gregory Gutin·Yaping Mao·Donglei Du·Xiaoyan Zhang
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Abstract

Given a natural number $k\ge 2$, we consider the $k$-submodular cover problem ($k$-SC). The objective is to find a minimum cost subset of a ground set $\mathcal{X}$ subject to the value of a $k$-submodular utility function being at least a certain predetermined value $\tau$. For this problem, we design a bicriteria algorithm with a cost at most $O(1/\epsilon)$ times the optimal value, while the utility is at least $(1-\epsilon)\tau/r$, where $r$ depends on the monotonicity of $g$.

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Wenqi Wang, Gregory Gutin, Yaping Mao, Donglei Du, Xiaoyan Zhang. 2023-12-06. Streaming Algorithms for the $k$-Submodular Cover Problem. https://arxiv.org/abs/2312.03593

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