On the separability of stochastic geometric objects, with applications

Jie Xue, Yuan Li, Ravi Janardan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

In this paper, we study the linear separability problem for stochastic geometric objects under the well-known unipoint/multipoint uncertainty models. Let S = SR ∪ SB be a given set of stochastic bichromatic points, and define n = min{|SR|, |SB|} and N = max{|SR|, |SB|}. We show that the separable-probability (SP) of S can be computed in O(nNd-1) time for d ≥ 3 and O(min{nN log N, N N2}) time for d = 2, while the expected separation-margin (ESM) of S can be computed in O(nNd) time for d ≥ 2. In addition, we give an Ω(nNd-1) witness-based lower bound for computing SP, which implies the optimality of our algorithm among all those in this category. Also, a hardness result for computing ESM is given to show the difficulty of further improving our algorithm. As an extension, we generalize the same problems from points to general geometric objects, i.e., polytopes and/or balls, and extend our algorithms to solve the generalized SP and ESM problems in O(nNd) and O(nNd+1) time, respectively. Finally, we present some applications of our algorithms to stochastic convex-hull related problems.

Original languageEnglish (US)
Title of host publication32nd International Symposium on Computational Geometry, SoCG 2016
EditorsSandor Fekete, Anna Lubiw
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages62.1-62.16
ISBN (Electronic)9783959770095
DOIs
StatePublished - Jun 1 2016
Event32nd International Symposium on Computational Geometry, SoCG 2016 - Boston, United States
Duration: Jun 14 2016Jun 17 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume51
ISSN (Print)1868-8969

Other

Other32nd International Symposium on Computational Geometry, SoCG 2016
CountryUnited States
CityBoston
Period6/14/166/17/16

Keywords

  • Convex hull
  • Expected separation-margin
  • Linear separability
  • Separable-probability
  • Stochastic objects

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