Smallest k-enclosing rectangle revisited

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

Abstract

Given a set of n points in the plane, and a parameter k, we consider the problem of computing the minimum (perimeter or area) axis-aligned rectangle enclosing k points. We present the first near quadratic time algorithm for this problem, improving over the previous near-O(n5/2)-time algorithm by Kaplan et al. [23]. We provide an almost matching conditional lower bound, under the assumption that (min, +)-convolution cannot be solved in truly subquadratic time. Furthermore, we present a new reduction (for either perimeter or area) that can make the time bound sensitive to k, giving near O(nk) time. We also present a near linear time (1 + ε)-approximation algorithm to the minimum area of the optimal rectangle containing k points. In addition, we study related problems including the 3-sided, arbitrarily oriented, weighted, and subset sum versions of the problem.

Original languageEnglish (US)
Title of host publication35th International Symposium on Computational Geometry, SoCG 2019
EditorsGill Barequet, Yusu Wang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771047
DOIs
StatePublished - Jun 1 2019
Event35th International Symposium on Computational Geometry, SoCG 2019 - Portland, United States
Duration: Jun 18 2019Jun 21 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume129
ISSN (Print)1868-8969

Conference

Conference35th International Symposium on Computational Geometry, SoCG 2019
CountryUnited States
CityPortland
Period6/18/196/21/19

Keywords

  • Approximation algorithms
  • Conditional lower bounds
  • Geometric optimization
  • Outliers

ASJC Scopus subject areas

  • Software

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  • Cite this

    Chan, T. M., & Har-Peled, S. (2019). Smallest k-enclosing rectangle revisited. In G. Barequet, & Y. Wang (Eds.), 35th International Symposium on Computational Geometry, SoCG 2019 [23] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 129). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2019.23