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

TL;DR

This paper introduces a Fast Stochastic Greedy algorithm for the $k$-Submodular Cover problem, significantly improving efficiency and scalability in AI applications by reducing query complexity and providing strong approximation guarantees.

Contribution

The paper presents a novel stochastic greedy algorithm that enhances approximation quality and reduces query complexity for the $k$-Submodular Cover problem.

Findings

Achieves strong bicriteria approximation guarantees.

Reduces function evaluations compared to existing methods.

Highly scalable for large-scale AI applications.

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.