ON k-HULLS AND RELATED PROBLEMS.

Richard Cole, Micha Sharir, Chee Yap

Research output: Contribution to journalArticle

Abstract

For any set X of points (in any dimension) and any k equals 1, 2,. . . , we introduce the concept of the k-hull of X. The k-hull is the set of points p such that for any hyperplane containing p there are at least k points of X in each closed half-space determined by the hyperplane. Several computational problems related to k-hulls are studied here, including computing the k-hull and finding a point in the k-hull. Some of our algorithms are of interest in themselves because of the techniques employed; in particular, a 'parametric' searching technique is used in a nontrivial way.

Original languageEnglish (US)
Pages (from-to)61-77
Number of pages17
JournalSIAM Journal on Computing
Volume16
Issue number1
StatePublished - Feb 1987

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Hyperplane
Half-space
Set of points
Closed
Computing
Concepts

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

ON k-HULLS AND RELATED PROBLEMS. / Cole, Richard; Sharir, Micha; Yap, Chee.

In: SIAM Journal on Computing, Vol. 16, No. 1, 02.1987, p. 61-77.

Research output: Contribution to journalArticle

Cole, R, Sharir, M & Yap, C 1987, 'ON k-HULLS AND RELATED PROBLEMS.', SIAM Journal on Computing, vol. 16, no. 1, pp. 61-77.
Cole, Richard ; Sharir, Micha ; Yap, Chee. / ON k-HULLS AND RELATED PROBLEMS. In: SIAM Journal on Computing. 1987 ; Vol. 16, No. 1. pp. 61-77.
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