2017/09/09 by Tasuku Soma, Yuichi Yoshida, Soma, Tasuku +1
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.1709.02910
arxiv created 2017/09/09 · arxiv updated 2017/09/12
In monotone submodular function maximization, approximation guarantees based on the curvature of the objective function have been extensively studied in the literature. However, the notion of curvature is often pessimistic, and we rarely obtain improved approximation guarantees, even for very simple objective functions. In this paper, we provide a novel approximation guarantee by extracting an M^\natural-concave function h:2E → \mathbb R+, a notion in discrete convex analysis, from the objective function f:2E → \mathbb R+. We introduce the notion of h-curvature, which measures how much f deviates from h, and show that we can obtain a (1-γ/e-ε)-approximation to the problem of maximizing f under a cardinality constraint in polynomial time for any constant ε> 0. Then, we show that we can obtain nontrivial approximation guarantees for various problems by applying the proposed algorithm.