A New Method for Efficiently Generating Planar Graph Visibility Representations
 John M. Boyer
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Abstract
A planar graph visibility representation maps each vertex to a horizontal segment at a vertical position and each edge to a vertical segment at a horizontal position such that each edge segment terminates at the vertical positions of its endpoint vertices and intersects no other horizontal vertex segments. The first O(n) algorithms for producing visibility representations were presented in [4, 5]. These were based on preprocessing to compute both an stnumbering and the dual of the planar graph, which were then used with the combinatorial planar embedding to produce a visibility representation. Greater efficiency is obtained in [3] by eliminating the need for the planar graph dual and by reusing the precomputed stnumbering in the PQtree [1] algorithm.
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 Boyer, J., Myrvold, W. (2004) On the cutting edge: Simplified O(n) planarity by edge addition. Journal of Graph Algorithms and Applications 8: pp. 241273
 Jayakumar, R., Thulasiraman, K., Swamy, M.N.S. (1988) Planar embedding: Lineartime algorithms for vertex placement and edge ordering. IEEE Transactions on Circuits and Systems 35: pp. 334344 CrossRef
 Rosenstiehl, P., Tarjan, R. (1986) Rectilinear planar layouts and bipolar orientations of planar graphs. Discrete and Computational Geometry 1: pp. 343353
 Tamassia, R., Tollis, I.G. (1986) A unified approach to visibility representations of planar graphs. Discrete and Computational Geometry 1: pp. 321341
 Title
 A New Method for Efficiently Generating Planar Graph Visibility Representations
 Book Title
 Graph Drawing
 Book Subtitle
 13th International Symposium, GD 2005, Limerick, Ireland, September 1214, 2005. Revised Papers
 Pages
 pp 508511
 Copyright
 2006
 DOI
 10.1007/11618058_47
 Print ISBN
 9783540314257
 Online ISBN
 9783540316671
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 3843
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Editors

 Patrick Healy ^{(16)}
 Nikola S. Nikolov ^{(17)}
 Editor Affiliations

 16. Department of Computer Science and Information Systems, University of Limerick
 17. Department of CSIS, University of Limerick
 Authors

 John M. Boyer ^{(18)}
 Author Affiliations

 18. IBM Victoria Software Lab, Victoria, BC, Canada
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