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

Authors:
Taku Aratsu;Kouichi Hirata;Tetsuji Kuboyama
Affiliations:
Department of Artificial Intelligence, Kyushu Institute of Technology, Kawazu 680-4, Iizuka 820-8502, Japan. aratsu@dumbo.ai.kyutech.ac.jp;(Correspd.) Department of Artificial Intelligence, Kyushu Institute of Technology, Kawazu 680-4, Iizuka 820-8502, Japan. hirata@ai.kyutech.ac.jp;Computer Center, Gakushuin University, Mejiro 1-5-1, Toshima, Tokyo 171-8588, Japan. ori-JFI@tk.cc.gakushuin.ac.jp
Venue:
Fundamenta Informaticae
Year:
2010

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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.