Fast Stochastic Greedy Algorithm for $k$-Submodular Cover Problem
This work addresses efficiency issues in AI and combinatorial optimization tasks like influence maximization and sensor placement, offering a practical solution for large-scale applications, though it appears incremental as it builds on existing greedy methods.
The paper tackled the k-Submodular Cover problem, which suffers from weak approximation guarantees or high query complexity in existing algorithms, by proposing a Fast Stochastic Greedy algorithm that achieves strong bicriteria approximation and substantially lowers query complexity, making it scalable for large-scale AI applications.
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.