论文信息 - Every Set of Disjoint Line Segments Admits a Binary Tree

Every Set of Disjoint Line Segments Admits a Binary Tree

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.

Prosenjit Bose | Godfried T. Toussaint | Michael E. Houle

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