文章基本信息

标题：Optimal Streaming Algorithms for Submodular Maximization with Cardinality Constraints
本地全文：下载
作者：Naor Alaluf ; Alina Ene ; Moran Feldman 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：168
页码：6:1-6:19
DOI：10.4230/LIPIcs.ICALP.2020.6
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the problem of maximizing a non-monotone submodular function subject to a cardinality constraint in the streaming model. Our main contributions are two single-pass (semi-)streaming algorithms that use OÌf(k)â<.poly(1/Îµ) memory, where k is the size constraint. At the end of the stream, both our algorithms post-process their data structures using any offline algorithm for submodular maximization, and obtain a solution whose approximation guarantee is Î±/(1+Î±)-Îµ, where Î± is the approximation of the offline algorithm. If we use an exact (exponential time) post-processing algorithm, this leads to 1/2-Îµ approximation (which is nearly optimal). If we post-process with the algorithm of [Niv Buchbinder and Moran Feldman, 2019], that achieves the state-of-the-art offline approximation guarantee of Î± = 0.385, we obtain 0.2779-approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.1715 due to [Feldman et al., 2018]. One of our algorithms is combinatorial and enjoys fast update and overall running times. Our other algorithm is based on the multilinear extension, enjoys an improved space complexity, and can be made deterministic in some settings of interest.
关键词：Submodular maximization; streaming algorithms; cardinality constraint