Fast Bicriteria Approximation Algorithm for Minimum Cost Submodular Cover Problem

Canh V. Pham, Quat V. Phu, Dung T. K. Ha

Abstract: This paper studies the Minimum Cost Submodular Cover (\(\textsf{MCSC}\)) problem over the ground set of size n, which aims at finding a subset with the minimal cost required so that the utility submodular function exceeds a given threshold. The issue has recently attracted a lot of attention due to its applications in various domains of artificial intelligence and combination optimization. However, the best approximation algorithm for the problem requires an expensive query complexity of \(O(n^2)\) that may become infeasible for some applications with large data.