Three-Dimensional Orthogonal Graph Drawing with Optimal Volume

Authors:
Therese Biedl;Torsten Thiele;David R. Wood
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;Institut fur Informatik, Freie Universitat Berlin, Takustrasse 19, 14195 Berlin, Germany;Department of Mathematics and Statistics, and School of Computer Science, McGill University, Montreal, Quebec, H3A 2A7, Canada
Venue:
Algorithmica
Year:
2006

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Abstract

An orthogonal drawing of a graph is an embedding of the graph in the rectangular grid, with vertices represented by axis-aligned boxes, and edges represented by paths in the grid that only possibly intersect at common endpoints. In this paper we study three-dimensional orthogonal drawings and provide lower bounds for three scenarios: (1) drawings where the vertices have a bounded aspect ratio, (2) drawings where the surfaces of vertices are proportional to their degrees, and (3) drawings without any such restrictions. Then we show that these lower bounds are asymptotically optimal, by providing constructions that in all scenarios match the lower bounds within a constant factor.