A pairing technique for areaefficient orthogonal drawings (extended abstract)
 Achilleas Papakostas,
 Ioannis G. Tollis
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Abstract
An orthogonal drawing of a graph is a drawing such that vertices are placed on grid points and edges are drawn as sequences of vertical and horizontal segments. In this paper we present linear time algorithms that produce orthogonal drawings of graphs with n nodes. If the maximum degree is four, then the drawing produced by our first algorithm needs area no greater than 0.76n ^{2}, and introduces no more than 2n + 2 bends. Also, every edge of such a drawing has at most two bends. Our algorithm is based on forming and placing pairs of vertices of the graph. If the maximum degree is three, then the drawing produced by our second algorithm needs at most 1/4n ^{2} area, and at most ILn/2 + 2l + 1⌋ bends (⌊n/2⌋ + 3 bends, if the graph is biconnected), where l is the number of biconnected components that are leaves in the block tree. For biconnected graphs, this algorithm produces optimal drawings with respect to the number of bends (within a constant of two), since there is a lower bound of n/2 + 1 in the number of bends for orthogonal drawings of degree 3 graphs.
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 Title
 A pairing technique for areaefficient orthogonal drawings (extended abstract)
 Book Title
 Graph Drawing
 Book Subtitle
 Symposium on Graph Drawing, GD '96 Berkeley, California, USA, September 18–20, 1996 Proceedings
 Pages
 pp 355370
 Copyright
 1997
 DOI
 10.1007/3540624953_60
 Print ISBN
 9783540624950
 Online ISBN
 9783540680482
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1190
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
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 Editors
 Authors

 Achilleas Papakostas ^{(1)}
 Ioannis G. Tollis ^{(1)}
 Author Affiliations

 1. Dept. of Computer Science, The University of Texas at Dallas, 750830688, Richardson, TX
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