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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 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 con gurations of line segments where any such tree requires degree 3. We provide an O(n log n) time algorithm for constructing such a tree, and show that this is optimal. 1 Introduction Given a set ... (Update)
Context of citations to this paper: More
...in some special cases [17] Applications. An immediate consequence of Theorem 1 is a recent result of Bose, Houle, and Toussaint [3]. They show that for every set of disjoint line segments, the segment endpoint visibility graph contains an encompassing tree, which is...
Cited by: More
Pointed Binary Encompassing Trees - Hoffmann, Speckmann, Tóth (Correct)
Segment Endpoint Visibility Graphs are Hamiltonian - Hoffmann, Tóth (2002) (Correct)
Segment endpoint visibility graphs are Hamiltonian - Hoffmann, Toth (2002) (Correct)
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BibTeX entry: (Update)
P. Bose, M. E. Houle, and G. Toussaint, Every set of disjoint line segments admits a binary tree, Algorithms and computation (Beijing, http://citeseer.ist.psu.edu/415369.html More
@inproceedings{ bose94every,
author = "Bose and Houle and Toussaint",
title = "Every Set of Disjoint Line Segments Admits a Binary Tree",
booktitle = "{ISAAC}: 5th International Symposium on Algorithms and Computation (formerly {SIGAL} International Symposium on Algorithms), Organized by Special Interest Group on Algorithms ({SIGAL}) of the Information Processing Society of Japan ({IPSJ}) and the Technical Group on Theoretical Foundation of Computing of the Institute of Electronics, Information and Communication Engineers ({IEICE}))",
year = "1994",
url = "citeseer.ist.psu.edu/415369.html" }
Citations (may not include all citations):3972 Introduction to Algorithms (context) - Cormen, Leiserson et al. - 1990
1254 Computational Geometry: An Introduction (context) - Preparata, Shamos - 1985
537 Graph Theory with Applications (context) - Bondy, Murty - 1976
125 Art Gallery Theorems and Algorithms (context) - O'Rourke - 1987
50 Transitions in Geometric Minimum Spanning Trees (context) - Monma, Suri - 1992
26 Computing simple circuits from a set of line segments is NP-.. - Rappaport - 1987
26 Computing simple circuits from a set of line segments - Rappaport, Imai et al. - 1990
12 Hamiltonian triangulations and circumscribing polygons of di.. (context) - Mirzaian - 1992
12 A tight lower bound on the size of visibility graphs (context) - Shen, Edelsbrunner - 1987
9 Computing the constrained relative neighborhood graphs and c.. (context) - Su, Chang - 1991
8 Two segment classes with Hamiltonian visibility graphs (context) - O'Rourke, Rippel - 1994
6 Computing monotone simple circuits in the plane (context) - Avis, Rappaport - 1988
5 Growing a tree from its branches - Bose, Toussaint - 1995
4 Computational Geometry: Theory and Applications (context) - Urabe, Watanabe et al. - 1992
3 personal communication (context) - Rivera-Campo, Urrutia - 1992
3 Hamiltonian polygons and polyhedra (context) - Gr - 1994
2 algorithm for nding minimum spanning trees (context) - Yao, log - 1975
1 Ecient algorithms for inserting and deleting edges from tria.. (context) - ElGindy, Toussaint - 1985
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The Graham Scan Triangulates Simple Polygons - Kong, Everett, Toussaint (1991) (Correct)
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Optimal Algorithms for Computing the Minimum Distance.. - Toussaint, Bhattacharya (1981) (Correct)
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