Abstract
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.
Partially supported by an NSERC and a Killam Postdoctoral Fellowship
Partially supported by an NSERC Postgraduate Fellowship
Partially supported by an NSERC Research Grant and a B.C. Advanced Systems Institute Fellowship.
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© 1996 Springer-Verlag Berlin Heidelberg
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Bose, P., McAllister, M., Snoeyink, J. (1996). Optimal algorithms to embed trees in a point set. In: Brandenburg, F.J. (eds) Graph Drawing. GD 1995. Lecture Notes in Computer Science, vol 1027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021791
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DOI: https://doi.org/10.1007/BFb0021791
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