Abstract
Computing the edit distance between two strings is one of the most fundamental problems in computer science. The standard dynamic programming based algorithm computes the edit distance and edit script in O(n 2) time and space. Often the edit script is of more importance than the value of the edit distance. The Four Russian Algorithm [1] computes the edit distance in O(n 2/logn) time but does not address how to compute edit script within that runtime. Hirschberg [2] gave an algorithm to compute edit script in linear space but the runtime remained O(n 2). In this paper we present algorithms that compute both the edit script and edit distance in \(O(\frac{n^2}{\log n})\) time using O(n) space.
Chapter PDF
Similar content being viewed by others
References
Arlazarov, V.L., Dinic, E.A., Kronrod, M.A., Faradzev, I.A.: On economic con- struction of the transitive closure of a directed graph. Dokl. Akad. Nauk SSSR 194, 487–488 (1970)
Hirschberg, D.S.: Linear space algorithm for computing maximal common subsequences. Communications of the ACM 18(6), 341–343 (1975)
Horowitz, E., Sahni, S., Rajasekaran, S.: Computer Algorithms. Silicon Press (2008)
Needleman, S.B., Wunsch, C.D.: A general method applicable to the search for similarities in the amino acid sequence of two proteins. Journal of Molecular Biology 48(3), 443–453 (1970)
Smith, T.F., Waterman, M.S.: Identification of common molecular subsequences. Journal of Molecular Biology 147(1), 195–197 (1981)
Gotoh, O.: Alignment of three biological sequences with an efficient traceback procedure. Journal of Theoretical Biology 121(3), 327–337 (1986)
Huang, X., Hardison, R.C., Miller, W.: A space-efficient algorithm for local similarities. Computer Applications in the Biosciences 6(4), 373–381 (1990)
Gotoh, O.: Pattern matching of biological sequences with limited storage. Computer Applications in the Biosciences 3(1), 17–20 (1987)
Myers, E.W., Miller, W.: Optimal alignments in linear space. Computer Applications in the Biosciences 4(1), 11–17 (1988)
Edmiston, E., Wagner, R.A.: Parallelization of the dynamic programming algorithm for comparison of sequences, pp. 78–80 (1987)
Ranka, S., Sahni, S.: String editing on an simd hypercube multicomputer. Journal of Parallel and Distributed Computing 9(4), 411–418 (1990)
Rajko, S., Aluru, S.: Space and time optimal parallel sequence alignments. IEEE Transactions on Parallel and Distributed Systems 15(12), 1070–1081 (2004)
Gusfield, D.: Algorithms of Strings Trees and Sequences. Cambridge (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kundeti, V., Rajasekaran, S. (2008). Extending the Four Russian Algorithm to Compute the Edit Script in Linear Space. In: Bubak, M., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2008. ICCS 2008. Lecture Notes in Computer Science, vol 5101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69384-0_94
Download citation
DOI: https://doi.org/10.1007/978-3-540-69384-0_94
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69383-3
Online ISBN: 978-3-540-69384-0
eBook Packages: Computer ScienceComputer Science (R0)