Fast algorithms for computing the smallest k-enclosing disc

Sariel Har-Peled, Soham Mazumdar

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider the problem of finding, for a given n point set P in the plane and an integer k ≤ n, the smallest circle enclosing at least k points of P. We present a randomized algorithm that computes in O (nk) expected time such a circle, improving over all previously known algorithms. Since this problem is believed to require Ω(nk) time, we present a linear time δ-approximation algorithm that outputs a circle that contains at least k points of P, and of radius less than (1 + δ)ropt(P, k), where ropt(P,k) is the radius of the minimal disk containing at least k points of P. The expected running time of this approximation algorithm is O(n + n · min (1/kδ3 log2 1/δ, k)).

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsGiuseppe di Battista, Uri Zwick
PublisherSpringer-Verlag Berlin Heidelberg
Pages278-288
Number of pages11
ISBN (Print)3540200649, 9783540200642
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2832
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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