Abstract
We present O(nlogm) algorithms for a new class of problems termed self-normalised distance with don’t cares. The input is a pattern p of length m and text t of length n > m. The elements of these strings are either integers or wild card symbols. In the shift version, the problem is to compute \(\min_{\alpha}\sum_{j=0}^{m-1}(\alpha + p_j - t_{i+j})^2\) for all i, where wild cards do not contribute to the sum. In the shift-scale version, the objective is to compute \(\min_{\alpha,\beta}\sum_{j=0}^{m-1}(\alpha+ \beta p_j - t_{i+j})^2\) for all i, similarly. We show that the algorithms have the additional benefit of providing simple O(nlogm) solutions for the problems of exact matching with don’t cares, exact shift matching with don’t cares and exact shift-scale matching with don’t cares.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Abrahamson, K.: Generalized string matching. SIAM journal on Computing 16(6), 1039–1051 (1987)
Amir, A., Farach, M.: Efficient 2-dimensional approximate matching of half-rectangular figures. Information and Computation 118(1), 1–11 (1995)
Amir, A., Lipsky, O., Porat, E., Umanski, J.: Approximate matching in the L 1 metric. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 91–103. Springer, Heidelberg (2005)
Atallah, M.J.: Faster image template matching in the sum of the absolute value of differences measure. IEEE Transactions on Image Processing 10(4), 659–663 (2001)
Clifford, P., Clifford, R.: Simple deterministic wildcard matching. Information Processing Letters 101(2), 53–54 (2007)
Clifford, P., Clifford, R., Iliopoulos, C.S.: Faster algorithms for δ,γ-matching and related problems. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 68–78. Springer, Heidelberg (2005)
Clifford, R., Iliopoulos, C.: String algorithms in music analysis. Soft Computing 8(9), 597–603 (2004)
Cole, R., Hariharan, R.: Verifying candidate matches in sparse and wildcard matching. In: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 592–601 (2002)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)
Fischer, M., Paterson, M.: String matching and other products. In: Karp, R. (ed.) Proceedings of the 7th SIAM-AMS Complexity of Computation, pp. 113–125 (1974)
Indyk, P.: Faster algorithms for string matching problems: Matching the convolution bound. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, pp. 166–173 (1998)
Jain, R., Kasturi, R., Schunck, B.G.: Machine Vision. McGraw-Hill, New York (1995)
Kalai, A.: Efficient pattern-matching with don’t cares. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 655–656, Philadelphia, PA, USA (2002)
Kosaraju, S.R.: Efficient string matching. Manuscript (1987)
Lewis, J.P.: Fast template matching. In: Vision Interface, pp. 120–123 (1995)
Lipsky, O., Porat, E.: Approximate matching in the l ∞ metric. In: Consens, M.P., Navarro, G. (eds.) SPIRE 2005. LNCS, vol. 3772, pp. 91–103. Springer, Heidelberg (2005)
Mäkinen, V., Navarro, G., Ukkonen, E.: Transposition invariant string matching. Journal of Algorithms 56(2), 124–153 (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clifford, P., Clifford, R. (2007). Self-normalised Distance with Don’t Cares. In: Ma, B., Zhang, K. (eds) Combinatorial Pattern Matching. CPM 2007. Lecture Notes in Computer Science, vol 4580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73437-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-73437-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73436-9
Online ISBN: 978-3-540-73437-6
eBook Packages: Computer ScienceComputer Science (R0)