Abstract
Given strings X and Y the exact string matching problem is to find the occurrences of Y as a substring of X. An alternative formulation asks for the lexicographically consecutive set of suffixes of X that begin with Y. We introduce a generalization called string range matching where we want to find the suffixes of X that are in an arbitrary lexicographical range bounded by two strings Y and Z. The problem has applications in distributed suffix sorting, where Y and Z are themselves suffixes of X. Exact string matching can be solved in linear time and constant extra space under the standard comparison model. Our conjecture is that string range matching is a harder problem and cannot be solved within the same time–space complexity. In this paper, we trace the upper bound on the complexity of string range matching by describing algorithms that are within a logarithmic factor of the time–space complexity of exact string matching, as well as variants of the problem and the model that can be solved in linear time and constant extra space.
This research is partially supported by the Academy of Finland through grant 118653 (ALGODAN) and grant 250345 (CoECGR).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Burrows, M., Wheeler, D.J.: A block sorting lossless data compression algorithm. Technical Report 124, Digital Equipment Corporation, Palo Alto, California (1994)
Crochemore, M.: String-matching on ordered alphabets. Theor. Comp. Sci. 92, 33–47 (1992)
Crochemore, M., Perrin, D.: Two-way string matching. J. ACM 38(3), 651–675 (1991)
Crochemore, M., Rytter, W.: Squares, cubes, and time-space efficient string searching. Algorithmica 13(5), 405–425 (1995)
Faro, S., Lecroq, T.: The exact online string matching problem: A review of the most recent results. ACM Comp. Surv. 45(2), 13 (2013)
Ferragina, P., Gagie, T., Manzini, G.: Lightweight data indexing and compression in external memory. Algorithmica 63(3), 707–730 (2012)
Fine, N.J., Wilf, H.S.: Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc. 16(1), 109–114 (1965)
Galil, Z., Seiferas, J.: Saving space in fast string-matching. SIAM J. Comp. 9(2), 417–438 (1980)
Galil, Z., Seiferas, J.: Time-space optimal string matching. J. Comp. Sys. Sci. 26, 280–294 (1983)
Kärkkäinen, J.: Fast BWT in small space by blockwise suffix sorting. Theor. Comp. Sci. 387(3), 249–257 (2007)
Kärkkäinen, J., Kempa, D., Puglisi, S.J.: Crochemore’s string matching algorithm: Simplification, extensions, applications. In: Proc. PSC 2013, pp. 168–175. Czech Technical University (2013)
Knuth, D., Morris, J.H., Pratt, V.: Fast pattern matching in strings. SIAM J. Comp. 6(2), 323–350 (1977)
Manber, U., Myers, G.W.: Suffix arrays: a new method for on-line string searches. SIAM J. Comp. 22(5), 935–948 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Kärkkäinen, J., Kempa, D., Puglisi, S.J. (2014). String Range Matching. In: Kulikov, A.S., Kuznetsov, S.O., Pevzner, P. (eds) Combinatorial Pattern Matching. CPM 2014. Lecture Notes in Computer Science, vol 8486. Springer, Cham. https://doi.org/10.1007/978-3-319-07566-2_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-07566-2_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07565-5
Online ISBN: 978-3-319-07566-2
eBook Packages: Computer ScienceComputer Science (R0)