Journal of Graph Algorithms and Applications
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Special Issue on Selected Papers from the Seventeenth International Symposium on Graph Drawing, GD 2009
Drawing 3-Polytopes with Good Vertex Resolution
Vol. 15, no. 1, pp. 33-52, 2011. Regular paper.
Abstract We study the problem how to obtain a small drawing of a 3-polytope with Euclidean distance between any two points at least 1. The problem can be reduced to a one-dimensional problem, since it is sufficient to guarantee distinct integer x-coordinates. We develop an algorithm that yields an embedding with the desired property such that the polytope is contained inside a 2(n−2)×2 ×1 box. The constructed embedding can be scaled to a grid embedding whose x-coordinates are contained in [0,2(n−2)]. Furthermore, the point set of the embedding has a small spread, which differs from the best possible spread only by a multiplicative constant.
Submitted: December 2009.
Reviewed: September 2010.
Revised: October 2010.
Accepted: November 2010.
Final: November 2010.
Published: February 2011.