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

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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 is the string edit distance between their binary tree codes and h is the minimum height of the trees.
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157--171
Opis fizyczny
Bibliogr. 13 poz., wykr.
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Bibliografia
  • [1] Akutsu, T.: A relationship between edit distance for ordered trees and edit distance for Euler strings, Information Processing Letters 100, 2006, 105-109.
  • [2] Akutsu, T., Fukagawa, D., Takasu, A.: Approximating tree edit distance through string edit distance, Algorithmica 57, 2010, 325-348.
  • [3] Aratsu, T., Hirata, K., Kuboyama, T.: Sibling distance for rooted ordered trees, Proc. JSAI PAKDD 2008 Post-Workshop Proceedings, LNAI 5433, 2009, 99-110.
  • [4] Bille, P.: A survey on tree edit distance and related problems, Theoretical Computer Science 337, 2005, 217-239.
  • [5] Cormode, G., Muthukrishnan, S.: The string edit distance matching problem with moves, ACM Transactions on Algorithms 3, 2007, 1-19.
  • [6] Demaine, E. D., Mozes, S., Rossman, B., Weimann, O.: An optimal decomposition algorithm for tree edit distance, Proc. ICALP'07, LNCS 4596, 2007, 146-157.
  • [7] Garofalakis, M., Kumar, A.: XML stream processing using tree-edit distance embeddings, ACMTransactions on Database System 30, 2006, 279-332.
  • [8] Kailing, K., Kriegel, H.-P., Schönauer, S., Seidl, T.: Efficient similarity search for hierarchical data in large databases, Proc. EBDT'04, LNCS 2992, 2004, 676-693.
  • [9] Knuth, D. E.: The art of computer programing, Vol. 1, Fundamental algorithms (Third Edition), Addison-Wesley, 1997.
  • [10] Magniez, F., de RougemontM.: Property testing of regular tree languages, Algorithmica 42, 2007, 127-146.
  • [11] Valiente, G.: An efficient bottom-up distance between trees, Proc. SPIRE'01, 2001, 212-219.
  • [12] Yang, R., Kalnis, P., Tung, A. K. H.: Similarity evaluation on tree-structured data, Proc. SIGMOD'05, 2005, 754-765.
  • [13] Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems, SIAM J. Comput. 18, 1989, 1245-1262.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0010-0066
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