Improved Streaming Algorithm for Minimum Cost Submodular Cover Problem

Tan D. Tran, Canh V. Pham, Dung P. Trung, Uyen T. Nguyen

Abstract: This paper introduces an efficient streaming algorithm for a well-known Minimum cost Submodular Cover (\({\textsf{MSC}}\)) problem. Our algorithm makes \(O(\log n)\) passes over the ground set, takes \(O(n \log n)\) query complexity and returns a \((1/\epsilon , 1-\epsilon )\)-bicriteria approximation solution with the ground set of size n and the precise parameter \(\epsilon >0\). Therefore, it is better than the existing streaming algorithms in terms of both solution guarantees and query complexity. Besides the theoretical performance, the experiment results on two applications, Revenue Threshold and Coverage Threshold, further show the superiority of our algorithm with the state-of-the-art ones.