Abstract
Let A and B be strings with lengths m and n, respectively, over a finite integer alphabet. Two classic string mathing problems are computing the edit distance between A and B, and searching for approximate occurrences of A inside B. We consider the classic Levenshtein distance, but the discussion is applicable also to indel distance. A relatively new variant [8] of string matching, motivated initially by the nature of string matching in music, is to allow transposition invariance for A. This means allowing A to be “shifted” by adding some fixed integer t to the values of all its characters: the underlying string matching task must then consider all possible values of t. Mäkinen et al. [12,13] have recently proposed O(mn loglog m) and O(dn loglog m) algorithms for transposition invariant edit distance computation, where d is the transposition invariant distance between A and B, and an O(mn loglog m) algorithm for transposition invariant approximate string matching. In this paper we first propose a scheme to construct transposition invariant algorithms that depend on d or k. Then we proceed to give an O(n + d 3) algorithm for transposition invariant edit distance, and an O(k 2 n) algorithm for transposition invariant approximate string matching.
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
Chang, W.I., Lawler, E.L.: Sublinear approximate string matching and biological applications. Algorithmica 12, 327–344 (1994)
Eppstein, D., Galil, Z., Giancarlo, R., Italiano, G.F.: Sparse dynamic programming I: linear cost functions. Journal of ACM 39(3), 519–545 (1992)
Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. 16th ACM Symposium on Theory of Computing (STOC 1984), pp. 135–143 (1984)
Galil, Z., Park, K.: Dynamic programming with convexity, concavity and sparsity. Theoretical Computer Science 92, 49–76 (1992)
Hirschberg, D.S.: Algorithms for the longest common subsequence problem. Journal of ACM 24, 664–675 (1977)
Johnson, D.B.: A priority queue in which initialization and queue operations take O(loglog D) time. Mathematical Systems Theory 15, 295–309 (1982)
Jokinen, P., Tarhio, J., Ukkonen, E.: A comparison of approximate string matching algorithms. Software Practice & Experience 26(12), 1439–1458 (1996)
Lemström, K., Ukkonen, E.: Including interval encoding into edit distance based music comparison and retrieval. In: Proc. Symposium on Creative & Cultural Aspects and Applications of AI & Cognitive Science (AISB 2000), pp. 53–60 (2000)
Lemström, K., Navarro, G., Pinzon, Y.: Practical algorithms for transposition-invariant string-matching. Journal of Discrete Algorithms (to appear)
Landau, G.M., Vishkin, U.: Fast parallel and serial approximate string matching. Journal of Algorithms 10, 157–169 (1989)
Levenshtein, V.I.: Binary codes capable of correcting spurious insertions and deletions of ones (original in Russian). Russian Problemy Peredachi Informatsii 1, 12–25 (1965)
Mäkinen, V., Navarro, G., Ukkonen, E.: Algorithms for transposition invariant string matching. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 191–202. Springer, Heidelberg (2003)
Mäkinen, V., Navarro, G., Ukkonen, E.: Transposition invariant string matching. Journal of Algorithms (to appear)
Navarro, G.: Multiple approximate string matching by counting. In: Proc. 4th South American Workshop on String Processing (WSP 1997), pp. 125–139 (1997)
Navarro, G.: A guided tour to approximate string matching. ACM Computing Surveys 33(1), 31–88 (2001)
Sellers, P.: The theory and computation of evolutionary distances: pattern recognition. Journal of Algorithms 1, 359–373 (1980)
Ukkonen, E.: Algorithms for approximate string matching. Information and Control 64, 100–118 (1985)
van Emde Boas, P.: Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters 6, 80–82 (1977)
Wagner, R., Fisher, M.: The string-to-string correction problem. Journal of ACM 21(1), 168–173 (1974)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hyyrö, H. (2005). Restricted Transposition Invariant Approximate String Matching Under Edit Distance. In: Consens, M., Navarro, G. (eds) String Processing and Information Retrieval. SPIRE 2005. Lecture Notes in Computer Science, vol 3772. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11575832_29
Download citation
DOI: https://doi.org/10.1007/11575832_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29740-6
Online ISBN: 978-3-540-32241-2
eBook Packages: Computer ScienceComputer Science (R0)