Title: Nearest Embedded and Embedding Self-Nested Trees,
Abstract: Self-nested trees present a systematic form of redundancy in their subtrees
and thus achieve optimal compression rates by DAG compression. A method for
quantifying the degree of self-similarity of plants through self-nested trees
has been introduced by Godin and Ferraro in 2010. The procedure consists in
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.