k-Submodular Cover Problem with a Matroid Constraint

Xinru Li; Donglei Du; Qian Liu; Yang Zhou; Min Li

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arXiv · 2610.26989

k-Submodular Cover Problem with a Matroid Constraint

Xinru Li·Donglei Du·Qian Liu·Yang Zhou·Min Li

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Abstract

We investigate k-submodular cover problem with a matroid constraint on an n-element ground set V , which seeks k disjoint subsets of V with minimal cost, where their union is an independent set for some matroid defined on V and the k-submodular utility function surpasses a specified threshold. This problem generalizes the k-submodular cover problem and has a wide range of applications in artificial intelligence and combinatorial optimization. In this paper, we propose a matroid extended greedy algorithm for this problem, analyze its bi-criteria approximation ratio, and further derive an improved approximation ratio under the special case of unit costs.

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BibTeX RIS

Xinru Li, Donglei Du, Qian Liu, Yang Zhou, Min Li. 2026-10-19. k-Submodular Cover Problem with a Matroid Constraint. https://arxiv.org/abs/2610.26989

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