文章基本信息

标题：Submodular Optimization with Contention Resolution Extensions
本地全文：下载
作者：Benjamin Moseley ; Maxim Sviridenko
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：145
页码：1-17
DOI：10.4230/LIPIcs.APPROX-RANDOM.2019.3
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：This paper considers optimizing a submodular function subject to a set of downward closed constraints. Previous literature on this problem has often constructed solutions by (1) discovering a fractional solution to the multi-linear extension and (2) rounding this solution to an integral solution via a contention resolution scheme. This line of research has improved results by either optimizing (1) or (2). Diverging from previous work, this paper introduces a principled method called contention resolution extensions of submodular functions. A contention resolution extension combines the contention resolution scheme into a continuous extension of a discrete submodular function. The contention resolution extension can be defined from effectively any contention resolution scheme. In the case where there is a loss in both (1) and (2), by optimizing them together, the losses can be combined resulting in an overall improvement. This paper showcases the concept by demonstrating that for the problem of optimizing a non-monotone submodular subject to the elements forming an independent set in an interval graph, the algorithm gives a .188-approximation. This improves upon the best known 1/(2e)~eq .1839 approximation.
关键词：Submodular; Optimization; Approximation Algorithm; Interval Scheduling