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Fast String Matching in Stationary Ergodic Sources

Published online by Cambridge University Press:  12 September 2008

John Shawe-Taylor
John Shawe-Taylor
Affiliation:
Department of Computer Science, Royal Holloway and Bedford New College, University of London, Egham, Surrey TW20 0EX, UK e-mail: john@dcs.rhbnc.ac.uk
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Abstract

A connection is made between the theory of ergodicity and the expected complexity of string searching. In particular, a substring search algorithm is introduced which, when applied to searching in text that has been produced by an appropriate stationary ergodic source, has an expected running time of O((N/m + m)logm), for a text string of length N and search string of length m. Similar expected complexity results have been obtained before, but the analysis is performed in a significantly more general framework, which models with greater accuracy the statistics of many types of strings, including natural language. The analysis also sheds light on the performance of the Boyer-Moore algorithm and the Sunday algorithm when applied to natural language.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 415 - 427
Copyright
Copyright © Cambridge University Press 1996

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References

[1]Knuth, D. E., Morris, J. H. and Pratt, V. R. (1977) Fast pattern matching in strings. SIAM. J. Comput. 6 323–350.CrossRefGoogle Scholar
[2]Smit, G. V. (1982) A comparison of three string matching algorithms. Software - Practice & Experience 12 57–66.CrossRefGoogle Scholar
[3]Sunday, D. M. (1990) A very fast substring search algorithm. Comm. ACM 33 132–142.CrossRefGoogle Scholar
[4]Boyer, R. S. and Moore, J. S. (1977) A fast string searching algorithm. Comm. ACM 20 762–772.CrossRefGoogle Scholar
[5]Guibas, L. J. and Odlyzko, A. M. (1980) A new proof of the linearity of the Boyer-Moore string searching algorithm. SIAM J. Comput. 9 672–682.CrossRefGoogle Scholar
[6]Baeza-Yates, R. A. (1989) String searching algorithms revisited. Proc. Workshop in Algorithms and Data Structures. Lecture Notes in Computer Science 382, pp. 75–96. Springer-Verlag.Google Scholar
[7]Horspool, N. (1980) Practical fast searching in strings. Software - Practice & Experience 16 501–506.CrossRefGoogle Scholar
[8]Schaback, R. (1988) On the expected sublinearity of the Boyer-Moore algorithm. SIAM J. Comput. 17 648–658.CrossRefGoogle Scholar
[9]Yao, A. C-C. (1979) The complexity of pattern matching for a random string. SIAM J. Comput. 8 368–387.CrossRefGoogle Scholar
[10]Shannon, C. E. (1948) A mathematical theory of communication. Bell. Syst. Tech. J. 27 379–423, 623–656.CrossRefGoogle Scholar
[11]Kim, J. Y. and Shawe-Taylor, J. S. (1994) Fast expected string matching using an n-gram algorithm. Software - Practice & Experience 24 79–88.CrossRefGoogle Scholar
[12]Welsh, D. (1988) Codes and Cryptography. Oxford University Press.Google Scholar
[13]Billingsley, P. (1965) Ergodic Theory and Information. Wiley.Google Scholar
[14]Thomasian, A. J. (1960) An elementary proof of the AEP of information theory. Ann. Math. Statist. 31 452–456.CrossRefGoogle Scholar
[15]Kim, J. Y. and Shawe-Taylor, J. S. (1992) An approximate string matching algorithm. Theor. Comput. Sci. 92 107–117.CrossRefGoogle Scholar