Straight-Line Embeddings of Two Rooted Trees in the Plane

A. Kaneko, M. Kano
1999 Discrete & Computational Geometry  
We prove the following theorem: Let T 1 and T 2 be two disjoint rooted trees with roots v 1 and v 2 , respectively, and let P be a set of |T 1 ∪ T 2 | points in the plane in general position containing two specified points p 1 and p 2 . Then the union T 1 ∪ T 2 can be straight-line embedded onto P such that v 1 and v 2 correspond to p 1 and p 2 , respectively. Moreover, we give a O(n 2 log n) time algorithm for finding such an embedding, where n is the number of vertices contained in T 1 ∪ T 2 .
doi:10.1007/pl00009441 fatcat:rqsirivg2nclhol4wjdux2ggcq