Abstract
There is no known algorithm that solves the general case of approximate string matching problem with the extended edit distance, where the edit operations are: insertion, deletion, mismatch, and swap, in time o(nm), where n is the length of the text and m is the length of the pattern.
In the effort to study this problem, the edit operations where analysed independently. It turns out that the approximate matching problem with only the mismatch operation can be solved in time \(O(n\sqrt{m \log m})\). If the only edit operation allowed is the swap, then the problem can be solved in time O(n log mlog σ), where σ = min(m,|Σ|).
In this paper we show that the approximate string matching problem with the swap and mismatch as the edit operations, can be computed in time \(O(n\sqrt{m \log m})\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abrahamson, K.: Generalized string matching. SIAM J. Comp. 16(6), 1039–1051 (1987)
Amir, A., Cole, R., Hariharan, R., Lewenstein, M., Porat, E.: Overlay matching. Information and Computation 181(1), 57–74 (2003)
Amir, A., Lewenstein, M., Porat, E.: Faster algorithms for string matching with k mismatches. In: Proc. 11th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 794–803 (2000)
Amir, A., Lewenstein, M., Porat, E.: Approximate swapped matching. Information Processing Letters 83(1), 33–39 (2002)
Cole, R., Hariharan, R.: Approximate string matching: A faster simpler algorithm. In: Proc. 9th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 463–472 (1998)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press and McGraw-Hill (1992)
Crochemore, M., Rytter, W.: Text Algorithms. Oxford University Press, Oxford (1994)
Fischer, M.J., Paterson, M.S.: Sring matching and other products. In: Karp, R.M. (ed.) SIAM-AMS Proceedings of Complexity of Computation, vol. 7, pp. 133–125 (1974)
Landau, G.M., Vishkin, U.: Efficient string matching with k mismatches. Theoretical Computer Science 43, 239–249 (1986)
Landau, G.M., Vishkin, U.: Fast parallel and serial approximate string matching. Journal of Algorithms 10(2), 157–169 (1989)
Levenshtein, V.I.: Binary codes capable of correcting, deletions, insertions and reversals. Soviet Phys. Dokl. 10, 707–710 (1966)
Lowrance, R., Wagner, R.A.: An extension of the string-to-string correction problem. J. of the ACM, 177–188 (1975)
Wagner, R.A.: On the complexity of the extended string-to-string correction problem. In: Proc. 7th ACM STOC, pp. 218–223 (1975)
Weiner, P.: Linear pattern matching algorithm. In: Proc. 14 IEEE Symposium on Switching and Automata Theory, pp. 1–11 (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Amir, A., Eisenberg, E., Porat, E. (2004). Swap and Mismatch Edit Distance. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-30140-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23025-0
Online ISBN: 978-3-540-30140-0
eBook Packages: Springer Book Archive