Three-dimensional orthogonal graph drawing with optimal volume

Therese Biedl, Torsten Thiele, David R. Wood

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)233-255
Number of pages23
Issue number3
Publication statusPublished - 2006

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