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.
Cite
CITATION STYLE
Bose, P., Houle, M. E., & Toussaint, G. (1994). Every set of disjoint line segments admits a binary tree. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 834 LNCS, pp. 20–28). Springer Verlag. https://doi.org/10.1007/3-540-58325-4_162
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