Volume requirements of 3d upward drawings

Authors:
Emilio Di Giacomo;Giuseppe Liotta;Henk Meijer;Stephen K. Wismath
Affiliations:
Dip. di Ing. Elettronica e dell’Informazione, Università degli Studi di Perugia, Italy;Dip. di Ing. Elettronica e dell’Informazione, Università degli Studi di Perugia, Italy;School of Computing, Queen’s University, Kingston, Ontario, Canada;Dept. of Math. and Computer Science, University of Lethbridge, Canada
Venue:
GD'05 Proceedings of the 13th international conference on Graph Drawing
Year:
2005

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Abstract

This paper studies the problem of drawing directed acyclic graphs in three dimensions in the straight-line grid model, and so that all directed edges are oriented in a common (upward) direction. We show that there exists a family of outerplanar directed acyclic graphs whose volume requirement is super-linear. We also prove that for the special case of rooted trees a linear volume upper bound is achievable.