Abstract
Let a text string of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps, (i.e. t ′ℓ ← t ℓ+1 and t ′ℓ+1 ← t ℓ) where each element can participate in no more than one swap.
The Pattern Matching with Swaps problem is that of finding all locations i for which there exists a swapped version T′ of T where there is an exact matching of P in location i of T′.
It was recently shown that the Pattern Matching with Swaps problem has a solution in time O(nm 1/3 log m log2 σ), where σ = min(|Σ|, m). We consider some interesting special cases of patterns, namely, patterns where there is no length-one run, i.e. there are no a, b, c ∈ Σ where b # a and b # c and where the substring abc appears in the pattern. We show that for such patterns the pattern matching with swaps problem can be solved in time O(n log2 m).
Partially supported by NSF grant CCR-96-10170 and the Israel Ministry of Science and the Arts grants 6297 and 8560.
partially supported by NSF grants CCR-9305873 and CCR-9610238.
Partially supported by the Israel Ministry of Science and the Arts grant 8560.
Preview
Unable to display preview. Download preview PDF.
References
K. Abrahamson. Generalized string matching. SIAM J. Computing, 16(6):1039–1051, 1987.
A. Amir, Y. Aumann, G. Landau, M. Lewenstein, and N. Lewenstein.Pattern matching with swaps. Proc. 38th IEEE FOCS, pages 144–153, 1997.
A. Amir and M. Farach. Efficient 2-dimensional approximate matching of halfrectangular figures. Information and Computation, 118(1):1–11, April 1995.
R.S. Boyer and J.S. Moore. A fast string searching algorithm. Comm. ACM, 20:762–772, 1977.
M.J. Fischer and M.S. Paterson. String matching and other products. Complexity of Computation, R.M. Karp (editor), SIAM-AMS Proceedings, 7:113–125, 1974.
R. Karp, R. Miller, and A. Rosenberg. Rapid identification of repeated patterns in strings, arrays and trees. Symposium on the Theory of Computing, 4:125–136, 1972.
D.E. Knuth, J.H. Morris, and V.R. Pratt. Fast pattern matching in strings. SIAM J. Computing, 6:323–350, 1977.
S. Rao Kosaraju. Efficient string matching. Manuscript, 1987.
V. I. Levenshtein. Binary codes capable of correcting, deletions, insertions and reversals. Soviet Phys. Dokl., 10:707–710, 1966.
R. Lowrance and R. A. Wagner. An extension of the string-to-string correction problem. J. of the ACM, pages 177–183, 1975.
S. Muthukrishnan and H. Ramesh. String matching under a general matching relation. Information and Computation, 122(1):140–148, 1995.
A. Pentland. Invited talk. NSF Institutional Infrastructure Workshop, 1992.
R. Y. Pinter. Efficient string matching with don't care patterns. In Z. Galil A. Apostolico, editor, Combinatorial Algorithms on Words, volume 12, pages 11–29. NATO ASI Series F, 1985.
P. Weiner. Linear pattern matching algorithm. Proc. 14 IEEE Symposium on Switching and Automata Theory, pages 1–11, 1973.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Amir, A., Landau, G.M., Lewenstein, M., Lewensteint, N. (1998). Efficient special cases of pattern matching with swaps. In: Farach-Colton, M. (eds) Combinatorial Pattern Matching. CPM 1998. Lecture Notes in Computer Science, vol 1448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030791
Download citation
DOI: https://doi.org/10.1007/BFb0030791
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64739-3
Online ISBN: 978-3-540-69054-2
eBook Packages: Springer Book Archive