Abstract
A black box method was recently given that solves the problem of online approximate matching for a class of problems whose distance functions can be classified as being local. A distance function is said to be local if for a pattern P of length m and any substring T[i,i + m − 1] of a text T, the distance between P and T[i,i + m − 1] is equal to Σ j Δ(P[j], T[i + j − 1]), where Δ is any distance function between individual characters. We extend this line of work by showing how to tackle online approximate matching when the distance function is non-local. We give solutions which are applicable to a wide variety of matching problems including function and parameterised matching, swap matching, swap-mismatch, k-difference, k-difference with transpositions, overlap matching, edit distance/LCS, flipped bit, faulty bit and L 1 and L 2 rearrangement distances. The resulting unamortised online algorithms bound the worst case running time per input character to within a log factor of their comparable offline counterpart.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Amir, A., Aumann, Y., Benson, G., Levy, A., Lipsky, O., Porat, E., Skiena, S., Vishne, U.: Pattern matching with address errors: rearrangement distances. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 1221–1229 (2006)
Amir, A., Aumann, Y., Kapah, O., Levy, A., Porat, E.: Approximate string matching with address bit errors. In: Ferragina, P., Landau, G.M. (eds.) CPM 2008. LNCS, vol. 5029, pp. 118–129. Springer, Heidelberg (2008)
Amir, A., Aumann, Y., Lewenstein, M., Porat, E.: Function matching. SIAM Journal on Computing 35(5), 1007–1022 (2006)
Amir, A., Cole, R., Hariharan, R., Lewenstein, M., Porat, E.: Overlap matching. Inf. Comput. 181(1), 57–74 (2003)
Amir, A., Eisenberg, E., Porat, E.: Swap and mismatch edit distance. Algorithmica 45(1), 109–120 (2006)
Amir, A., Farach, M., Muthukrishnan, S.: Alphabet dependence in parameterized matching. Inf. Process. Lett. 49(3), 111–115 (1994)
Clifford, P., Clifford, R.: Self-normalised distance with don’t cares. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 63–70. Springer, Heidelberg (2007)
Clifford, R., Efremenko, K., Porat, B., Porat, E.: A black box for online approximate pattern matching. In: Ferragina, P., Landau, G.M. (eds.) CPM 2008. LNCS, vol. 5029, pp. 143–151. Springer, Heidelberg (2008)
Galil, Z.: String matching in real time. Journal of the ACM 28(1), 134–149 (1981)
Landau, G.M., Vishkin, U.: Fast string matching with k differences. J. Comput. Syst. Sci. 37(1), 63–78 (1988)
Levenshtein, I.V.: Binary codes capable of correcting deletions, insertions, and reversals. Cybernetics and Control Theory (1966)
Masek, W.J., Paterson, M.: A faster algorithm computing string edit distances. J. Comput. Syst. Sci. 20(1), 18–31 (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clifford, R., Sach, B. (2009). Online Approximate Matching with Non-local Distances. In: Kucherov, G., Ukkonen, E. (eds) Combinatorial Pattern Matching. CPM 2009. Lecture Notes in Computer Science, vol 5577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02441-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-02441-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02440-5
Online ISBN: 978-3-642-02441-2
eBook Packages: Computer ScienceComputer Science (R0)