Abstract
Our results on regular and minimum-crossing projections of line segments have immediate corollaries for polygonal chains, polygons, trees and more general geometric graphs in 3-D since these are all special cases of sets of line segments. Our results also have application to graph drawing for knot-theorists. Let K be a knot with n vertices. To study the knot's combinatorial properties, knot theorists obtain a planar graph G called the diagram of K by a regular projection of K. Many of their algorithms are applied to G and therefore their time complexity depends on the space complexity of G. By combining our algorithms we can obtain regular projections with the minimum number of crossings thereby minimizing the time complexity of their algorithms.
Research of the first author was supported by an NSERC & Killam Fellowship. Research of the second and third authors was carried out during their visit to McGill University in 1995 and was self-supported. The fourth author was supported by NSERC Grant no. OGP0009293 and FCAR Grant no. 93-ER-0291.
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Bose, P., Ramos, P., Gomez, F., Toussaint, G. (1996). Drawing nice projections of objects in space. In: Brandenburg, F.J. (eds) Graph Drawing. GD 1995. Lecture Notes in Computer Science, vol 1027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021790
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DOI: https://doi.org/10.1007/BFb0021790
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