P. Bose, M. E. Houle, and G.T. Toussaint, Every set of disjoint line segments admits a binary tree, Discrete Comput Geom. 26 (2001), 387--410. Home/Search Document Details and Download
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Segment Endpoint Visibility Graphs are Hamiltonian - Hoffmann, Tóth (2002) (Correct)
....whether a set S admits an alternating Hamiltonian polygon, if the segments of S are allowed to intersect at endpoints [16] although it can be decided efficiently 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 defined as a planar embedding of a tree with maximal degree three that contains all segment edges. Indeed, a Hamiltonian polygon together with all segment edges ....
....relies only on elementary geometry, like ray shooting, convex hull, or sorting angles. Based on our proof, it is straightforward to give an O(n log n) algorithm to find a Hamiltonian polygon for a given set of line segments. This running time is asymptotically optimal, as was shown by Bose et al. [3] for finding an encompassing tree; such a tree can be obtained from a Hamiltonian polygon in linear time, as explained above. The rest of the paper is organized as follows. In Section 2, we prove Theorem 1 by induction. The key lemma of the proof, Lemma 3, is proved algorithmically in three ....
P. Bose, M. E. Houle, and G. T. Toussaint, Every set of disjoint line segments admits a binary tree, Discrete Comput. Geom. 26 (2001), 387--410.
Pointed Binary Encompassing Trees - Hoffmann, Speckmann, Tóth (Correct)
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P. Bose, M. E. Houle, and G.T. Toussaint, Every set of disjoint line segments admits a binary tree, Discrete Comput Geom. 26 (2001), 387--410.
Segment endpoint visibility graphs are Hamiltonian - Hoffmann, Toth (2002) (Correct)
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P. Bose, M. E. Houle, and G. Toussaint, Every set of disjoint line segments admits a binary tree, Algorithms and computation (Beijing,
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