Approximation Algorithms for Non-Submodular Optimization Over Sliding Windows

Abstract

In this paper, the problem we study is how to maximize a monotone non-submodular function with cardinality constraint. Different from the previous streaming algorithms, this paper mainly considers the sliding window model. Based on the concept of diminishing-return ratio [Formula: see text], we propose a [Formula: see text]-approximation algorithm with the memory [Formula: see text], where [Formula: see text] is the ratio between maximum and minimum values of any singleton element of function [Formula: see text]. Then, we improve the approximation ratio to [Formula: see text] through the sub-windows at the expense of losing some memory. Our results generalize the corresponding results for the submodular case.