Drawing Non-Layered Tidy Trees In Linear Time

A. J. Van Der Ploeg 1
1 ATEAMS - Analysis and Transformation based on rEliAble tool coMpositionS
Inria Lille - Nord Europe, CWI - Centrum Wiskunde & Informatica
Abstract : The well-known Reingold-Tilford algorithm produces tidy-layered drawings of trees: drawings where all nodes at the same depth are vertically aligned. However, when nodes have varying heights, layered drawing may use more vertical space than necessary. A non-layered drawing of a tree places children at a fixed distance from the parent, thereby giving a more vertically compact drawing. Moreover, non-layered drawings can also be used to draw trees where the vertical position of each node is given, by adding dummy nodes. In this paper, we present the first linear-time algorithm for producing non-layered drawings. Our algorithm is a modification of the Reingold-Tilford algorithm, but the original complexity proof of the Reingold-Tilford algorithm uses an invariant that does not hold for the non-layered case. We give an alternative proof of the algorithm and its extension to non-layered drawings. To improve drawings of trees of unbounded degree, extensions to the Reingold-Tilford algorithm have been proposed. These extensions also work in the non-layered case, but we show that they then cause a O(n2) run-time. We then propose a modification to these extensions that restores the O(n) run-time.
Type de document :
Article dans une revue
Software: Practice and Experience, Wiley, 2013
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Contributeur : Tijs Van Der Storm <>
Soumis le : jeudi 2 janvier 2014 - 17:06:07
Dernière modification le : mercredi 29 novembre 2017 - 15:06:18


  • HAL Id : hal-00923389, version 1



A. J. Van Der Ploeg. Drawing Non-Layered Tidy Trees In Linear Time. Software: Practice and Experience, Wiley, 2013. 〈hal-00923389〉



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