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Journal Articles Algorithms Year : 2019

Nearest embedded and embedding self-nested trees


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.
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Dates and versions

hal-01584078 , version 1 (08-09-2017)
hal-01584078 , version 2 (28-08-2019)



Romain Azaïs. Nearest embedded and embedding self-nested trees. Algorithms, 2019, 12 (9), pp.1-16. ⟨10.3390/a12090180⟩. ⟨hal-01584078v2⟩
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