Abstract
Given two strings S and T, together with an integer representing the similarity bound, the characteristic string problem consists in finding the shortest substrings of T such that S has no substrings similar to them, in the sense that one string is similar to another if the amount of ‘dissimilarities’ between them is less than or equal to the similarity bound. Under the similarity criterion that uses Levenshtain distance to measure the amount of dissimilarities between two strings, this problem is known to be solvable in cubic time and linear space. The present article proposes a new algorithm for this problem that performs in almost quadratic time and almost linear space, under a certain class of similarity criteria, including the similarity criterion based on Levenshtain distance.
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
Dan, G., Fleischer, R., Gąsieniek, L., Gunopulos, D., Kärkkäinen, J.: Episode Matching. In: Hein, J., Apostolico, A. (eds.) CPM 1997. LNCS, vol. 1264, pp. 12–27. Springer, Heidelberg (1997)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences – Computer Science and Computational Biology. Cambridge University Press (1997)
Hamming, R.W.: Error detecting and error correcting codes. Bell Syst. Tech. J. 29, 147–160 (1950)
Ito, M., Shimizu, K., Nakanishi, M., Hashimoto, A.: Polynomial-Time Algorithms for Computing Characteristic Strings. In: Crochemore, M., Gusfield, D. (eds.) CPM 1994. LNCS, vol. 807, pp. 274–288. Springer, Heidelberg (1994)
Landau, G.M., Vishkin, U.: Introducing efficient parallelism into approximate string matching and a new serial algorithm. In: 18th Annual ACM Symposium on Theory of Computing, pp. 220–230 (1986)
Levenshtain, V.I.: Binary codes capable of correcting insertions and reversals. Sov. Phys. Dokl. 10, 707–710 (1966)
MaaĂŸ, M.G.: A fast algorithm for the inexact characteristic string problem. Technical Report TUM-I0312, Fakultät fĂ¼r Informatik, TU MĂ¼nchen (2003)
Myers, E.W.: An o(nd) difference algorithm and its variations. Algorithmica 1, 251–266 (1986)
Nakanishi, M., Hasidume, M., Ito, M., Hashimoto, A.: A Linear-Time Algorithm for Computing Characteristic Strings. In: Du, D.-Z., Zhang, X.-S. (eds.) ISAAC 1994. LNCS, vol. 834, pp. 315–323. Springer, Heidelberg (1994)
Saiki, R., Gelfand, D., Stoffel, S., Scharf, S., Higuchi, R., Horn, G., Mullis, K., Erlich, H.: Primer-directed enzymatic amplification of DNA with a thermostable DNA polymerase. Sci. 239, 487–491 (1988)
Sakai, Y.: An almost quadratic time algorithm for sparse spliced alignment. Theory Comput. Syst. 48, 189–210 (2011)
Sakai, Y.: A fast algorithm for multiplying min-sum permutations. Discrete Appl. Math. 159, 2175–2183 (2011)
Tiskin, A.: Semi-local string comparison: Algorithmic techniques and applications. Math. Comput. Sci. 1, 571–603 (2008)
Tiskin, A.: Fast distance multiplication of unit-Monge matrices. In: 21st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1287–1295 (2010)
Ukkonen, E.: On-line construction of suffix-trees. Algorithmica 14, 249–260 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sakai, Y. (2011). A New Algorithm for the Characteristic String Problem under Loose Similarity Criteria. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_68
Download citation
DOI: https://doi.org/10.1007/978-3-642-25591-5_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25590-8
Online ISBN: 978-3-642-25591-5
eBook Packages: Computer ScienceComputer Science (R0)