Approximation of trees by self-nested trees

TL;DR

This paper explores the properties of self-nested trees, offering a new combinatorial characterization, and introduces an approximation algorithm for efficiently predicting edit distances between trees.

Contribution

It provides a new combinatorial characterization of self-nested trees and an approximation algorithm for fast tree similarity assessment.

Findings

Self-nested trees enable faster query responses than general trees.

The approximation algorithm effectively predicts edit distances.

Self-nested trees have significant compression advantages.

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.