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Open AccessArticle

Nearest Embedded and Embedding Self-Nested Trees

Laboratoire Reproduction et Développement des Plantes, Univ Lyon, ENS de Lyon, UCB Lyon 1, CNRS, INRA, Inria, F-69342 Lyon, France
Algorithms 2019, 12(9), 180; https://doi.org/10.3390/a12090180
Received: 25 June 2019 / Revised: 23 August 2019 / Accepted: 27 August 2019 / Published: 29 August 2019
(This article belongs to the Special Issue Data Compression Algorithms and their Applications)
Self-nested trees present a systematic form of redundancy in their subtrees and thus achieve optimal compression rates by directed acrylic graph (DAG) compression. A method for quantifying the degree of self-similarity of plants through self-nested trees was introduced by Godin and Ferraro in 2010. The procedure consists of computing a self-nested approximation, called the nearest embedding self-nested tree, that both embeds the plant and is the closest to it. In this paper, we propose a new algorithm that computes the nearest embedding self-nested tree with a smaller overall complexity, but also the nearest embedded self-nested tree. We show from simulations that the latter is mostly the closest to the initial data, which suggests that this better approximation should be used as a privileged measure of the degree of self-similarity of plants. View Full-Text
Keywords: unordered trees; self-nested trees; approximation of trees; structural self-similarity unordered trees; self-nested trees; approximation of trees; structural self-similarity
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Azaïs, R. Nearest Embedded and Embedding Self-Nested Trees. Algorithms 2019, 12, 180.

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