Optimal algorithms to embed trees in a point set

  • Prosenjit Bose
  • Michael McAllister
  • Jack Snoeyink
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1027)


We present optimal Θ(n log n) time algorithms to solve two tree embedding problems whose solution previously took quadratic time or more: rooted-tree embeddings and degree-constrained embeddings. In the rooted-tree embedding problem we are given a rooted-tree T with n nodes and a set of n points P with one designated point p and are asked to find a straight-line embedding of T into P with the root at point p. In the degree-constrained embedding problem we are given a set of n points P where each point is assigned a positive degree and the degrees sum to 2n}-2 and are asked to embed a tree in P using straight lines that respects the degrees assigned to each point of P. In both problems, the points of P must be in general position and the embeddings have no crossing edges.


Convex Hull Geographic Information System Tree Edge Embedding Problem Maintenance Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Michael McAllister
    • 1
  • Jack Snoeyink
    • 1
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

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