P. Bose and G. T. Toussaint, Growing a tree from its branches, J. Algorithms 19 (1995), 86--103. Home/Search Document Details and Download
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On Removing Extrinsic Degeneracies in Computational.. - Gómez.. (Correct)
....vertical line sweep algorithms two points with the same x coordinate constitute an algorithm induced degeneracy. Computational geometers make these assumptions because doing so makes it not only much easier to design algorithms but often yields algorithms with reduced worst case complexities (see [7], for example) On the other hand, to the implementers of geometric algorithms these assumptions are frustrating. Programmers would like the algorithms to work for any input that they may encounter in practice, regardless of the degeneracies such an input contains. In this paper, we discuss ....
P. Bose and G. Toussaint. Growing a tree from its branches. Journal of Algorithms, 19:86--103, 1995.
Every Set of Disjoint Line Segments Admits a Binary Tree - Bose, Houle, Toussaint (3 citations) Self-citation (Bose Toussaint) (Correct)
....of disjoint line segments such that each line segment is an edge of the tree and the tree has no crossing edges such a tree will be referred to as an encompassing tree. The problem of determining whether a set of line segments admits an encompassing tree was first studied by Bose and Toussaint [3], who showed that a set of disjoint line segments always admits an encompassing tree. In addition, they showed that the encompassing tree of minimum total edge length has maximum degree 7. Subsequently, Rivera Campo and Urrutia [10] proved that a disjoint set of line segments always admits an ....
P. Bose and G. Toussaint. Growing a Tree from its Branches, Proc. of the First Pacific Conference on Computer Graphics and Applications, Vol 1, pp. 91--103, Pacific Graphics `93, Seoul, South Korea, September 1993.
Proximity Graphs on Line Segments - Bose, Toussaint Self-citation (Bose Toussaint) (Correct)
....n is the number of line segments and r is the number of reflex vertices of the simple polygon. Several other algorithms, variations and extensions have been studied since [Ber88, CR90, GR91, Jun88, KM92, MV93, Sei88, Slo91, Wan93, WT92] Both Jennings and Lingas [JL92] and Bose and Toussaint [BT92] independently showed that the Euclidean minimum spanning tree of a set of disjoint line segments is crossing free. In fact, Chew [Che87, Che89] pointed out that the constrained Euclidean minimum spanning tree is a subgraph of the constrained Delaunay triangulation. A natural extension to these ....
....has been algorithmic. There has been some work done in characterizing proximity graphs of point sets (see [LS93, BBL93, BBL94, GDBL94, FHM93, MJMar, MQar] but almost no work has been done from a graph theoretic point of view for proximity graphs of line segments. The paper of Bose and Toussaint [BT92], who showed that the maximum degree of the Euclidean minimum spanning tree of a set of disjoint line segments is at most seven, seems to be the only work that has addressed these problems to date. There are many open problems in this area. We conclude with a few of them. 1. What is the maximum ....
P. Bose and G. Toussaint. Growing a tree from its branches. In Proc. First Pacific Conf. on Computer Grapics and Appl., pages 91--103, 1993 Also available as: McGill Technical Report no. SOCS 92.12, McGill University, 1992.
Every Set of Disjoint Line Segments Admits a Binary Tree - Bose, Houle, Toussaint (3 citations) Self-citation (Bose Toussaint) (Correct)
....Quebec, H3A 2A7, CANADA. Email: godfried cs.mcgill.ca. 1 Figure 1: no encompassing tree with maximum degree 2 such a tree will be referred to as an encompassing tree. The problem of determining whether a set of line segments admits an encompassing tree was rst studied by Bose and Toussaint [3], who showed that a set of disjoint line segments always admits an encompassing tree, and that the encompassing tree of minimum total edge length has maximum degree 7. Subsequently, RiveraCampo and Urrutia [14] proved that a disjoint set of line segments always admits an encompassing tree with ....
P. Bose and G. Toussaint, Growing a tree from its branches, J. Algorithms 19 (1995), 86-103.
Pointed Binary Encompassing Trees - Hoffmann, Speckmann, Tóth (Correct)
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P. Bose and G. T. Toussaint, Growing a tree from its branches, J. Algorithms 19 (1995), 86--103.
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