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Every set of disjoint line segments admits a binary tree

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Algorithms and Computation (ISAAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 834))

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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 end-points 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.

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Authors and Affiliations

  1. School of Computer Science, McGill University, Montréal, Québec, Canada

    Prosenjit Bose & Godfried Toussaint

  2. Dept. of Computer Science, University of Newcastle, 2308, Newcastle, NSW, Australia

    Michael E. Houle

Authors
  1. Prosenjit Bose
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  2. Michael E. Houle
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  3. Godfried Toussaint
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Editor information

Ding-Zhu Du Xiang-Sun Zhang

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© 1994 Springer-Verlag Berlin Heidelberg

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Bose, P., Houle, M.E., Toussaint, G. (1994). Every set of disjoint line segments admits a binary tree. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_162

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  • DOI: https://doi.org/10.1007/3-540-58325-4_162

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58325-7

  • Online ISBN: 978-3-540-48653-4

  • eBook Packages: Springer Book Archive

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