Simple multi-pass streaming algorithms for skyline points and extreme points

Chan, TM and Rahul, S (2021) Simple multi-pass streaming algorithms for skyline points and extreme points. In: 38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021, 16 -19 March 2021, Virtual, Saarbrucken.

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Abstract

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 logO(1) n) space and O(logd n) 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.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to the Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Keywords:	Convex hull; Extreme points; Multi-pass streaming algorithms; Randomized algorithms; Skyline
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	26 Nov 2023 08:11
Last Modified:	26 Nov 2023 08:11
URI:	https://eprints.iisc.ac.in/id/eprint/82993

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