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, Iizuka, Japan 820-8502;Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka, Japan 820-8502;Computer Center, Gakushuin University, Tokyo, Japan 171-8588
Venue:
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Year:
2009

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Abstract

In this paper, we give an approximation of the tree edit distance through the string edit distance for binary tree codes, instead of one 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, σ is the string edit distance between their binary tree codes and h is the minimum height of the trees.