Optimal line bipartitions of point sets

Olivier Devillers, Matthew J. Katz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Let S be a set of n points in the plane. We study the following problem: Partition S by a line into two subsets S a and S b such that max {f(Sa), f(Sb)} is minimal, where f is any monotone function defined over 2S. We first present a solution to the case where the points in S are the vertices of some convex polygon and apply it to some common cases — f(S′) is the perimeter, area, or width of the convex hull of S′ ⊆ S — to obtain linear solutions (or O(n log n) solutions if the convex hull of S is not given) to the corresponding problems. This solution is based on an efficient procedure for finding a minimal entry in matrices of some special type, which we believe is of independent interest. For the general case we present a linear space solution which is in some sense output sensitive. It yields solutions to the perimeter and area cases that are never slower and often faster than the best previous solutions.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings
EditorsTetsuo Asano, Yoshihide Igarashi, Hiroshi Nagamochi, Satoru Miyano, Subhash Suri
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540620486, 9783540620488
StatePublished - 1 Jan 1996
Externally publishedYes
Event7th International Symposium on Algorithms and Computation, ISAAC 1996 - Osaka, Japan
Duration: 16 Dec 199618 Dec 1996

Publication series

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


Conference7th International Symposium on Algorithms and Computation, ISAAC 1996

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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