Maximization of Constrained Non-submodular Functions

Abstract

We investigate a non-submodular maximization problem subject to a p-independence system constraint, where the non-submodularity of the utility function is characterized by a series of parameters, such as submodularity (supmodularity) ratio, generalized curvature, and zero order approximate submodularity coefficient, etc. Inspired by Feldman et al. [15] who consider a non-monotone submodular maximization with a p-independence system constraint, we extend their Repeat-Greedy algorithm to non-submodular setting. While there is no general reduction to convert algorithms for submodular optimization problems to non-submodular optimization problems, we are able to show the extended Repeat-Greedy algorithm has an almost constant approximation ratio for non-monotone non-submodular maximization.