Upward point set embeddability for convex point sets is in P

Authors:
Michael Kaufmann;Tamara Mchedlidze;Antonios Symvonis
Affiliations:
Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany;Dept. of Mathematics, National Technical University of Athens, Greece;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany
Venue:
GD'11 Proceedings of the 19th international conference on Graph Drawing
Year:
2011

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Abstract

In this paper, we present a polynomial dynamic programming algorithm that tests whether a n-vertex directed tree T has an upward planar embedding into a convex point-set S of size n. We also note that our approach can be extended to the class of outerplanar digraphs. This nontrivial and surprising result implies that any given digraph can be efficiently tested for an upward planar embedding into a given convex point set.