Fast Stochastic Greedy Algorithm for $k$-Submodular Cover Problem

• URL: http://arxiv.org/abs/2511.00869v1
• Date: Sun, 02 Nov 2025 09:39:06 GMT
• Title: Fast Stochastic Greedy Algorithm for $k$-Submodular Cover Problem
• Authors: Hue T. Nguyen, Tan D. Tran, Nguyen Long Giang, Canh V. Pham,
• Abstract summary: Existing algorithms for $k$SC often provide weak approximation guarantees or prohibitively high query complexity.<n>Our approach reduces the number of function evaluations, making it highly scalable and practical for large-scale real-world applications.
• Score: 2.8348950186890467
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the $k$-Submodular Cover ($kSC$) problem, a natural generalization of the classical Submodular Cover problem that arises in artificial intelligence and combinatorial optimization tasks such as influence maximization, resource allocation, and sensor placement. Existing algorithms for $\kSC$ often provide weak approximation guarantees or incur prohibitively high query complexity. To overcome these limitations, we propose a \textit{Fast Stochastic Greedy} algorithm that achieves strong bicriteria approximation while substantially lowering query complexity compared to state-of-the-art methods. Our approach dramatically reduces the number of function evaluations, making it highly scalable and practical for large-scale real-world AI applications where efficiency is essential.

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