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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