Algorithms for the constrained editing distance between ordered labeled trees and related problems

Abstract This paper considers the problem of computing a constrained editing distance between ordered labeled trees. This distance metric can be applied to pattern recognition, syntactic tree comparison, classification tree comparison and other applications. The problem of approximate ordered tree matching is also considered. We present optimal algorithms for solving these problems in sequential time O (| T 1 | × | T 2 |

[1]  Shin-Yee Lu,et al.  Waveform Correlation by Tree Matching , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Alfred V. Aho,et al.  Bounds on the Complexity of the Longest Common Subsequence Problem , 1976, J. ACM.

[3]  Kuo-Chung Tai,et al.  The Tree-to-Tree Correction Problem , 1979, JACM.

[4]  Michael J. Fischer,et al.  The String-to-String Correction Problem , 1974, JACM.

[5]  Tao Jiang,et al.  Some MAX SNP-Hard Results Concerning Unordered Labeled Trees , 1994, Inf. Process. Lett..

[6]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[7]  Kaizhong Zhang,et al.  On the Editing Distance Between Unordered Labeled Trees , 1992, Inf. Process. Lett..

[8]  Stanley M. Selkow,et al.  The Tree-to-Tree Editing Problem , 1977, Inf. Process. Lett..

[9]  Gad M. Landau,et al.  Fast Parallel and Serial Approximate String Matching , 1989, J. Algorithms.

[10]  Esko Ukkonen,et al.  Finding Approximate Patterns in Strings , 1985, J. Algorithms.

[11]  Peter H. Sellers,et al.  The Theory and Computation of Evolutionary Distances: Pattern Recognition , 1980, J. Algorithms.

[12]  P. Sellers.  On the Theory and Computation of Evolutionary Distances , 1974 .

[13]  Bruce A. Shapiro,et al.  An algorithm for comparing multiple RNA secondary structures , 1988, Comput. Appl. Biosci..

[14]  Kaizhong Zhang,et al.  Simple Fast Algorithms for the Editing Distance Between Trees and Related Problems , 1989, SIAM J. Comput..

[15]  Kaizhong Zhang,et al.  Approximate Tree Matching in the Presence of Variable Length Don't Cares , 1994, J. Algorithms.

[16]  Heikki Mannila,et al.  Ordered and Unordered Tree Inclusion , 1995, SIAM J. Comput..

[17]  Kaizhong Zhang,et al.  Comparing multiple RNA secondary structures using tree comparisons , 1990, Comput. Appl. Biosci..

[18]  Shin-Yee Lu.  A Tree-to-Tree Distance and Its Application to Cluster Analysis , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.