Abstract
We study the fundamental problem of pattern matching in the case where the string data is weighted: for every position of the string and every letter of the alphabet a probability of occurrence for this letter at this position is given. Sequences of this type are commonly used to represent uncertain data. They are of particular interest in computational molecular biology as they can represent different kind of ambiguities in DNA sequences: distributions of SNPs in genomes populations; position frequency matrices of DNA binding profiles; or even sequencing-related uncertainties. A weighted string may thus represent many different strings, each with probability of occurrence equal to the product of probabilities of its letters at subsequent positions. In this article, we present new average-case results on pattern matching on weighted strings and show how they are applied effectively in several biological contexts. A free open-source implementation of our algorithms is made available.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Amir, A., Chencinski, E., Iliopoulos, C.S., Kopelowitz, T., Zhang, H.: Property matching and weighted matching. Theor. Comput. Sci. 395(2–3), 298–310 (2008)
Amir, A., Iliopoulos, C., Kapah, O., Porat, E.: Approximate matching in weighted sequences. In: Lewenstein, M., Valiente, G. (eds.) CPM 2006. LNCS, vol. 4009, pp. 365–376. Springer, Heidelberg (2006). doi:10.1007/11780441_33
Barton, C., Iliopoulos, C.S., Pissis, S.P.: Optimal computation of all tandem repeats in a weighted sequence. Algorithms Mol. Biol. 9(21), 1–12 (2014)
Barton, C., Kociumaka, T., Pissis, S.P., Radoszewski, J.: Efficient index for weighted sequences. In: CPM 2016, LIPIcs, vol. 54, pp. 4: 1–4: 13. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2016)
Barton, C., Liu, C., Pissis, S.P.: Fast average-case pattern matching on weighted sequences. CoRR abs/1512.01085 (2015). (submitted to IPL)
Barton, C., Pissis, S.P.: Linear-time computation of prefix table for weighted strings. In: Manea, F., Nowotka, D. (eds.) WORDS 2015. LNCS, vol. 9304, pp. 73–84. Springer, Heidelberg (2015). doi:10.1007/978-3-319-23660-5_7
Caspi, R., Helinski, D.R., Pacek, M., Konieczny, I.: Interactions of DnaA proteins from distantly related bacteria with the replication origin of the broad host range plasmid RK2. J. Biol. Chem. 275(24), 18454–18461 (2000)
Chang, W.I., Marr, T.G.: Approximate string matching and local similarity. In: Crochemore, M., Gusfield, D. (eds.) CPM 1994. LNCS, vol. 807, pp. 259–273. Springer, Heidelberg (1994). doi:10.1007/3-540-58094-8_23
Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on Strings. Cambridge University Press, New York (2007)
Farach, M.: Optimal suffix tree construction with large alphabets. In: FOCS 1997, pp. 137–143. IEEE Computer Society (1997)
Guo, Y., Jamison, D.C.: The distribution of SNPs in human gene regulatory regions. BMC Genom. 6(1), 1–11 (2005)
Hattori, M., et al.: The DNA sequence of human chromosome 21. Nature 405, 311–319 (2000)
Huang, L., Popic, V., Batzoglou, S.: Short read alignment with populations of genomes. Bioinformatics 29(13), 361–370 (2013)
Kociumaka, T., Pissis, S.P., Radoszewski, J.: Pattern matching and consensus problems on weighted sequences and profiles. In: ISAAC 2016, LIPIcs. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2016)
Lovász, L., Pelikán, J., Vesztergombi, K.: Discrete Mathematics: Elementary and Beyond. Springer, New York (2003)
Musser, D.R.: Introspective sorting and selection algorithms. Softw. Pract. Exp. 27(8), 983–993 (1997)
Pizzi, C., Ukkonen, E.: Fast profile matching algorithms - a survey. Theor. Comput. Sci. 395(2–3), 137–157 (2008)
Sandelin, A., Alkema, W., Engström, P., Wasserman, W.W., Lenhard, B.: JASPAR: an open-access database for eukaryotic transcription factor binding profiles. Nucleic Acids Res. 32(1), D91–D94 (2004)
Varela, M.A., Amos, W.: Heterogeneous distribution of SNPs in the human genome: microsatellites as predictors of nucleotide diversity and divergence. Genomics 95(3), 151–159 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Barton, C., Liu, C., Pissis, S.P. (2016). On-Line Pattern Matching on Uncertain Sequences and Applications. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_40
Download citation
DOI: https://doi.org/10.1007/978-3-319-48749-6_40
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48748-9
Online ISBN: 978-3-319-48749-6
eBook Packages: Computer ScienceComputer Science (R0)