文章基本信息

标题：Simple Multi-Pass Streaming Algorithms for Skyline Points and Extreme Points
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作者：Chan, Timothy M. ; Rahul, Saladi
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：187
页码：22:1-22:14
DOI：10.4230/LIPIcs.STACS.2021.22
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In this paper, we present simple randomized multi-pass streaming algorithms for fundamental computational geometry problems of finding the skyline (maximal) points and the extreme points of the convex hull. For the skyline problem, one of our algorithm occupies O(h) space and performs O(log n) passes, where h is the number of skyline points. This improves the space bound of the currently best known result by Das Sarma, Lall, Nanongkai, and Xu [VLDB'09] by a logarithmic factor. For the extreme points problem, we present the first non-trivial result for any constant dimension greater than two: an O(h log^{O(1)}n) space and O(log^dn) pass algorithm, where h is the number of extreme points. Finally, we argue why randomization seems unavoidable for these problems, by proving lower bounds on the performance of deterministic algorithms for a related problem of finding maximal elements in a poset.
关键词：multi-pass streaming algorithms; skyline; convex hull; extreme points; randomized algorithms