Two Algorithms for Three Dimensional Orthogonal Graph DrawingEades, Peter and Symvonis, Antonios and Whitesides, Sue (1997) Two Algorithms for Three Dimensional Orthogonal Graph Drawing. In: Symposium on Graph Drawing, GD '96, September 1820, 1996 , pp. 139154(Official URL: http://dx.doi.org/10.1007/3540624953_44). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540624953_44
AbstractWe use basic results from graph theory to design two algorithms for constructing 3dimesional, intersectionfree orthogonal grid drawings of n vertex graphs of maximum degree 6. Our first algorithm gives drawings bounded by an O(\sqrt(n)) \times O(\sqrt(n)) \times O(\sqrt(n)) box; each edge route containing at most 7 bends. The best previous result generated edge routes containing up to 16 bends per route. Our second algorithm gives drawings having at most 3 bends per edge route. The drawings lie in an O(n) \times O(n) \times O(n) bounding box. Together , the two algorithms initiate the study of bends/bounding box tradeoff issues for 3dimensional grid drawings.
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