Computing the smallest k-enclosing circle and related problems

Alon Efrat, Micha Sharir, Alon Ziv

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

5 Scopus citations


We present an efficient algorithm for solving the “smallest kenclosing circle” (kSC) problem: Given a set of n points in the plane and an integer k ≤ n, find the smallest disk containing k of the points. We present several algorithms that run in O(nk logc n) time, where the constant c depends on the storage that the algorithm is allowed. When using O(nk) storage, the problem can be solved in time O(nklog2 n). When only O(n log n) storage is allowed, the running time is (formula presentd). The method we describe can be easily extended to obtain efficient solutions of several related problems (with similar time and storage bounds). These related problems include: finding the smallest homothetic copy of a given convex polygon P, which contains k points from a given planar set, and finding the smallest hypodrome of a given length and orientation (formally defined in Section 4) containing k points from a given planar set.

Original languageEnglish (US)
Title of host publicationAlgorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Nicola Santoro, Sue Whitesides
Number of pages12
ISBN (Print)9783540571551
StatePublished - 1993
Event3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada
Duration: Aug 11 1993Aug 13 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume709 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other3rd Workshop on Algorithms and Data Structures, WADS 1993

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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