Approximation of trees by self-nested trees

Abstract

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of trees. In particular, we show from both theoretical and practical viewpoints that complex queries can be quickly answered in self-nested trees compared to general trees. We also present an approximation algorithm of a tree by a self-nested one that can be used in fast prediction of edit distance between two trees.

treex: a Python package for manipulating rooted trees

“…Concerning the latter two, coding processes (Pitman, 2006) have been implemented, as well as DAG compression (Godin & Ferraro, 2010). In addition, comparison between trees can be performed via an edit distance algorithm (Azais, Durand, & Godin, 2019). Self-nested approximations of trees (Godin & Ferraro, 2010, Azais (2017, ) have been implemented through different algorithms.…”

Enumeration of Irredundant Forests

“…They simply check whether the current tree has n vertices or not, and as their expansion rule adds one vertex at a time, they decide to cut a branch in the enumeration tree once they have reached n vertices. Similarly, adding a vertex to a tree can only increase its height or outdegree, so we can proceed in the same way to enumerate all trees with maximal height H and maximal outdegree d. Indeed, the number of trees satisfying those constraints is finite [4,Appendix D.2].…”