Almost Optimal Semi-streaming Maximization for k-Extendible Systems

Abstract

In this paper we consider the problem of finding a maximum weight set subject to a $k$-extendible constraint in the data stream model. The only non-trivial algorithm known for this problem to date---to the best of our knowledge---is a semi-streaming $k^2(1+\epsilon )$-approximation algorithm (Crouch and Stubbs, 2014), but semi-streaming $O(k)$-approximation algorithms are known for many restricted cases of this general problem. In this paper, we close most of this gap by presenting a semi-streaming $O(k\log k)$-approximation algorithm for the general problem, which is almost the best possible even in the offline setting (Feldman et al., 2017).

17 pages, 1 figure

References in corpus (1)

• A $(k+3)/2$-approximation algorithm for monotone submodular maximization over a $k$-exchange system