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Handbook of Graph Drawing and Visualization
book

Handbook of Graph Drawing and Visualization

by Roberto Tamassia
August 2013
Intermediate to advanced content levelIntermediate to advanced
862 pages
32h 20m
English
Chapman and Hall/CRC
Content preview from Handbook of Graph Drawing and Visualization
78 CHAPTER 2. CROSSINGS AND PLANARIZATION
estimating the number of the produced crossings, ar e relatively simply. The hard part is to
show a matching lower bound in order to deduce the approximation factor.
In 2007, Gitler et al. s howed in [GHLS08] that cr(G) is approximable within a factor of
4.5∆
2
when considering projective graphs, i.e., graphs that are embeddable in the projective
plane. One may think of such a projective plane as a large circular area A, on which to draw
the graph without any cros si ngs . Any line leaving A re-enters A exactly at the opposite
position. Consequently, any vertex drawn on the border of A is mirrored on the opposite
side as well. The key idea of the approximation algorithm now is to take such a drawing,
paste
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Publisher Resources

ISBN: 9781420010268