Refinement of Orthogonal Graph Drawings
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Compact Encodings of Planar Orthogonal Drawings
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Dissections and trees, with applications to optimal mesh encoding and to random sampling
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Schnyder woods and orthogonal surfaces
GD'06 Proceedings of the 14th international conference on Graph drawing
Optimal coding and sampling of triangulations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Optimal placement of ad-hoc devices under a VCG-style routing protocol
ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
Algorithms and theory of computation handbook
An application of well-orderly trees in graph drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Minimum-width grid drawings of plane graphs
Computational Geometry: Theory and Applications
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The author introduces a method to optimize the required area, minimum angle and number of bends of planar drawings of graphs on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. With this method linear time and space algorithms can be designed for many graph drawing problems. He shows that every triconnected planar graph G can be drawn convexly with straight lines on an (2n-4)*(n-2) grid. If G has maximum degree four (three), then G can be drawn orthogonal with at most (/sup 3n///sub 2/)+3 (at most (/sup n///sub 2/)+1) bends on an n*n grid ((/sup n///sub 2/)*(/sup n///sub 2/) grid, respectively). If G has maximum degree d, then G can be drawn planar on an (2n-6)*(3n-6) grid with minimum angle larger than /sup 1///sub d-2/ radians and at most 5n-15 bends. These results give in some cases considerable improvements over previous results, and give new bounds in other cases. Several other results, e.g. concerning visibility representations, are included.