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Optimal Algorithms to Embed Trees in a Point Set

Bose, Prosenjit and McAllister, Michael and Snoeyink, Jack (1996) Optimal Algorithms to Embed Trees in a Point Set. [Conference Paper]

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Abstract

We present optimal \Theta(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.

Item Type:Conference Paper
Classifications:P Styles > P.720 Straight-line
G Algorithms and Complexity > G.490 Embeddings
M Methods > M.900 Tree
ID Code:138
Deposited By:Maciejak, Agnes
Deposited On:12 Oct 2004
Last Modified:18 Sep 2008 13:08

Repository Staff Only: item control page

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