k-Submodular Cover Problem: Application and Algorithms

In this paper, we investigate a novel combinatorial optimization, k-Submodular Cover, as follows: Given a finite set V, a monotone k-submodular function , and a threshold . The problem aim at finding a solution with the size is minimal so that the function . This problem is a general version of the well-known Submodular Cover problem and thus it is NP-hard. Two efficient algorithms for the k-Submodular Cover problem are proposed. The first one is Greedy algorithm and the second one is a Streaming algorithm with theoretical guarantees. Extensive experiments on real-world datasets show that the proposed algorithms are more effective than the state-of-the-art methods in the application of Influence Threshold with k topics. In particular, our streaming algorithm not only provides a guaranteed theoretical solution, but also proves to be superior to the rest of the algorithms in terms of running time.