Upward point-set embeddability

Authors:
Markus Geyer;Michael Kaufmann;Tamara Mchedlidze;Antonios Symvonis
Affiliations:
Wilhelm-Schickard, Institut für Informatik, Universität Tübingen, Tübingen, Germany;Wilhelm-Schickard, Institut für Informatik, Universität Tübingen, Tübingen, Germany;Dept. of Mathematics, National Technical University of Athens, Athens, Greece;Dept. of Mathematics, National Technical University of Athens, Athens, Greece
Venue:
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Year:
2011

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Abstract

We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a given upward planar digraph D has an upward planar embedding into a point set S. We show that any switch tree admits an upward planar straight-line embedding into any convex point set. For the class of k-switch trees, that is a generalization of switch trees (according to this definition a switch tree is a 1-switch tree), we show that not every k-switch tree admits an upward planar straight-line embedding into any convex point set, for any k ≥ 2. Finally we show that the problem of Upward Point-Set Embeddability is NP-complete.