Approximating Tree Edit Distance through String Edit Distance for Binary Tree Codes

Abstract

This article proposes an approximation of the tree edit distance through the string edit distance for binary tree codes, instead of for Euler strings introduced by Akutsu (2006). Here, a binary tree code is a string obtained by traversing a binary tree representation with two kinds of dummy nodes of a tree in preorder. Then, we show that σ/2 ≤ τ ≤ (h + 1)σ + h, where τ is the tree edit distance between trees, and σ is the string edit distance between their binary tree codes and h is the minimum height of the trees.