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Theoretical and empirical comparisons of approximate string matching algorithms

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Combinatorial Pattern Matching (CPM 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 644))

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Abstract

We study in depth a model of non-exact pattern matching based on edit distance, which is the minimum number of substitutions, insertions, and deletions needed to transform one string of symbols to another. More precisely, the k differences approximate string matching problem specifies a text string of length n, a pattern string of length m, the number k of differences (substitutions, insertions, deletions) allowed in a match, and asks for all locations in the text where a match occurs. We have carefully implemented and analyzed various O(kn) algorithms based on dynamic programming (DP), paying particular attention to dependence on b the alphabet size. An empirical observation on the average values of the DP tabulation makes apparent each algorithm's dependence on b. A new algorithm is presented that computes much fewer entries of the DP table. In practice, its speedup over the previous fastest algorithm is 2.5X for binary alphabet; 4X for four-letter alphabet; 10X for twenty-letter alphabet. We give a probabilistic analysis of the DP table in order to prove that the expected running time of our algorithm (as well as an earlier “cut-off” algorithm due to Ukkonen) is O(kn) for random text. Furthermore, we give a heuristic argument that our algorithm is O(kn/(√b-1)) on the average, when alphabet size is taken into consideration.

This research was conducted at the University of California, Berkeley, and was supported in part by Department of Energy grant DE-FG03-90ER60999

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Author information

Authors and Affiliations

  1. Cold Spring Harbor Laboratory, 11724, Cold Spring Harbor, NY

    William I. Chang

  2. University of Washington, 98195, Seattle, WA

    Jordan Lampe

Authors
  1. William I. Chang
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  2. Jordan Lampe
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Editor information

Alberto Apostolico Maxime Crochemore Zvi Galil Udi Manber

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© 1992 Springer-Verlag Berlin Heidelberg

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Chang, W.I., Lampe, J. (1992). Theoretical and empirical comparisons of approximate string matching algorithms. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds) Combinatorial Pattern Matching. CPM 1992. Lecture Notes in Computer Science, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56024-6_14

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  • DOI: https://doi.org/10.1007/3-540-56024-6_14

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  • Print ISBN: 978-3-540-56024-1

  • Online ISBN: 978-3-540-47357-2

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