Improved Bounds for Drawing Trees on Fixed Points with L-Shaped Edges

Biedl, Therese and Chan, Timothy M. and Derka, Martin and Jain, Kshitij and Lubiw, Anna (2017) Improved Bounds for Drawing Trees on Fixed Points with L-Shaped Edges. In: Graph Drawing and Network Visualization. GD 2017, September 25-27 , pp. 305-317(Official URL: https://doi.org/10.1007/978-3-319-73915-1_24).

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Abstract

Let T be an n-node tree of maximum degree 4, and let P be a set of n points in the plane with no two points on the same horizontal or vertical line. It is an open question whether T always has a planar drawing on P such that each edge is drawn as an orthogonal path with one bend (an “L-shaped” edge). By giving new methods for drawing trees, we improve the bounds on the size of the point set P for which such drawings are possible to: O(n^1.55) for maximum degree 4 trees; O(n1.22) for maximum degree 3 (binary) trees; and O(n^1.142) for perfect binary trees. Drawing ordered trees with L-shaped edges is harder—we give an example that cannot be done and a bound of O(nlogn) points for L-shaped drawings of ordered caterpillars, which contrasts with the known linear bound for unordered caterpillars.

Item Type: Conference Paper
Classifications: M Methods > M.900 Tree
P Styles > P.600 Poly-line > P.600.300 Mainly Orthogonal
URI: http://gdea.informatik.uni-koeln.de/id/eprint/1611

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