Every set of disjoint line segments admits a binary tree

Prosenjit Bose, Michael E. Houle, Godfried Toussaint

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

Abstract

Given a set of n disjoint line segments in the plane, we show that it is always possible to form a tree with the endpoints of the segments such that each line segment is an edge of the tree, the tree has no crossing edges, and the maximum vertex degree of the tree is 3. Furthermore, there exist configurations of line segments where any such tree requires at least degree 3. We provide an O(n log n) time algorithm for constructing such a tree, and show that this is optimal.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings
PublisherSpringer-Verlag
Pages20-28
Number of pages9
ISBN (Print)9783540583257
StatePublished - Jan 1 1994
Event5th Annual International Symposium on Algorithms and Computation, ISAAC 1994 - Beijing, China
Duration: Aug 25 1994Aug 27 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume834 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th Annual International Symposium on Algorithms and Computation, ISAAC 1994
CountryChina
CityBeijing
Period8/25/948/27/94

Fingerprint

Binary trees
Binary Tree
Line segment
Disjoint
Vertex Degree
Configuration

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Bose, P., Houle, M. E., & Toussaint, G. (1994). Every set of disjoint line segments admits a binary tree. In Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings (pp. 20-28). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 834 LNCS). Springer-Verlag.

Every set of disjoint line segments admits a binary tree. / Bose, Prosenjit; Houle, Michael E.; Toussaint, Godfried.

Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings. Springer-Verlag, 1994. p. 20-28 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 834 LNCS).

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

Bose, P, Houle, ME & Toussaint, G 1994, Every set of disjoint line segments admits a binary tree. in Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 834 LNCS, Springer-Verlag, pp. 20-28, 5th Annual International Symposium on Algorithms and Computation, ISAAC 1994, Beijing, China, 8/25/94.
Bose P, Houle ME, Toussaint G. Every set of disjoint line segments admits a binary tree. In Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings. Springer-Verlag. 1994. p. 20-28. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Bose, Prosenjit ; Houle, Michael E. ; Toussaint, Godfried. / Every set of disjoint line segments admits a binary tree. Algorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings. Springer-Verlag, 1994. pp. 20-28 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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