Trees with Convex Faces and Optimal Angles

Carlson, Josiah and Eppstein, David (2007) Trees with Convex Faces and Optimal Angles. In: Graph Drawing 14th International Symposium, GD 2006, September 18-20, 2006, Karlsruhe, Germany , pp. 77-88 (Official URL: http://dx.doi.org/10.1007/978-3-540-70904-6_9).

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Abstract

We consider drawings of trees in which all edges incident to leaves can be extended to infinite rays without crossing, partitioning the plane into infinite convex polygons. Among all such drawings we seek the one maximizing the angular resolution of the drawing. We find linear time algorithms for solving this problem, both for plane trees and for trees without a fixed embedding. In any such drawing, the edge lengths may be set independently of the angles, without crossing; we describe multiple strategies for setting these lengths.

Item Type:Conference Paper
Additional Information:10.1007/978-3-540-70904-6_9
Classifications:M Methods > M.900 Tree
G Algorithms and Complexity > G.070 Area / Edge Length
ID Code:763

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References

G. Liotta and H. Meijer. Voronoi drawings of trees. Computational Geometry: Theory and Applications, 24(3):147-178, 2003.

S. Malitz. On the angular resolution of planar graphs. In Proc. 24th ACM Symp. Theory of Computing, pages 527-538, 1992.