Abstract
Because of its connection to the well-known \(\mathcal{NP}\)-complete shortest superstring combinatorial optimization problem, the Sequence Assembly Problem (SAP) has been formulated in simple and sometimes unrealistic string and graph-theoretic frameworks. This paper revisits this problem by re-examining the relationship between the most common formulations of the SAP and their computational tractability under different theoretical frameworks. For each formulation we show examples of logically-consistent candidate solutions which are nevertheless unfeasible in the context of the underlying biological problem. This material is hoped to be valuable to theoreticians as they develop new formulations of SAP as well as of guidance to developers of new pipelines and algorithms for sequence assembly and variant detection.
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
Preview
Unable to display preview. Download preview PDF.
References
Armen, C., Stein, C.: A 2 2/3-approximation algorithm for the shortest superstring problem. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 87–101. Springer, Heidelberg (1996)
Bradnam, K., et al.: Assemblathon 2: evaluating de novo methods of genome assembly in three vertebrate species. GigaScience 2(1), 10 (2013)
Church, A., Rosser, J.B.: Some properties of conversion. Transactions of the American Mathematical Society 39(3), 472–482 (1936)
Earl, D.A., et al.: Assemblathon 1: A competitive assessment of de novo short read assembly methods. Genome Research (2011)
Gallant, J., Maier, D., Astorer, J.: On finding minimal length superstrings. Journal of Computer and System Sciences 20(1), 50–58 (1980)
Gnerre, S., et al.: High-quality draft assemblies of mammalian genomes from massively parallel sequence data. Proceedings of the National Academy of Sciences 108(4), 1513–1518 (2011)
Hierholzer, C., Wiener, C.: Ueber die mglichkeit, einen linienzug ohne wiederholung und ohne unterbrechung zu umfahren. Mathematische Annalen 6(1), 30–32 (1873)
Iqbal, Z., Caccamo, M., Turner, I., Flicek, P., McVean, G.: De novo assembly and genotyping of variants using colored de bruijn graphs. Nature Genetics 44(2), 226–232 (2012)
Karp, R.M.: The role of algorithmic research in computational genomics. In: Computational Systems Bioinformatics Conf, p. 10. IEEE Computer Society (2003)
Kingsford, C., Schatz, M., Pop, M.: Assembly complexity of prokaryotic genomes using short reads. BMC Bioinformatics 11(1), 21 (2010)
Koren, S., et al.: Hybrid error correction and de novo assembly of single-molecule sequencing reads. Nature Biotechnology 30(7), 693–700 (2012)
Li, R., et al.: De novo assembly of human genomes with massively parallel short read sequencing. Genome Research 20(2), 265–272 (2010)
Li, S., Li, R., Li, H., Lu, J., Li, Y., Bolund, L., Schierup, M., Wang, J.: Soapindel: Efficient identification of indels from short paired reads. Genome Research (2012)
Mardis, E.R.: The impact of next-generation sequencing technology on genetics. Trends in Genetics 24(3), 133–141 (2008)
Medvedev, P., Georgiou, K., Myers, G., Brudno, M.: Computability of models for sequence assembly. In: Giancarlo, R., Hannenhalli, S. (eds.) WABI 2007. LNCS (LNBI), vol. 4645, pp. 289–301. Springer, Heidelberg (2007)
Myers, E.W.: Toward simplifying and accurately formulating fragment assembly. Journal of Computational Biology 2, 275–290 (1995)
Myers, E.W.: The fragment assembly string graph. Bioinformatics 21(suppl. 2), ii79–ii85 (2005)
Nagarajan, N., Pop, M.: Parametric complexity of sequence assembly: theory and applications to next generation sequencing. Journal of Computational Biology 16(7), 897–908 (2009)
Narzisi, G., Mishra, B.: Comparing de novo genome assembly: The long and short of it. PLoS ONEÂ 6(4), e19175 (2011)
Narzisi, G., Mishra, B.: Scoring-and-unfolding trimmed tree assembler: concepts, constructs and comparisons. Bioinformatics 27(2), 153–160 (2011)
Narzisi, G., O’Rawe, J.A., Iossifov, I.: ha Lee, Y., Wang, Z., Wu, Y., Lyon, G.J., Wigler, M., Schatz, M.C.: Accurate detection of de novo and transmitted indels within exome-capture data using micro-assembly. bioRxiv (2013)
Rittel, H.W.J., Webber, M.M.: Dilemmas in a general theory of planning. Policy Sciences 4, 155–169 (1973)
Roberts, R., Carneiro, M., Schatz, M.: The advantages of smrt sequencing. Genome Biology 14(7), 405 (2013)
Smith, T.F., Waterman, M.S.: Identification of common molecular subsequences. Journal of Molecular Biology 147(1), 195–197 (1981)
Tarhio, J., Ukkonen, E.: A greedy approximation algorithm for constructing shortest common superstrings. Theor. Comput. Sci. 57(1), 131–145 (1988)
Turner, J.S.: Approximation algorithms for the shortest common superstring problem. Inf. Comput. 83(1), 1–20 (1989)
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
Narzisi, G., Mishra, B., Schatz, M.C. (2014). On Algorithmic Complexity of Biomolecular Sequence Assembly Problem. In: Dediu, AH., MartÃn-Vide, C., Truthe, B. (eds) Algorithms for Computational Biology. AlCoB 2014. Lecture Notes in Computer Science(), vol 8542. Springer, Cham. https://doi.org/10.1007/978-3-319-07953-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-07953-0_15
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07952-3
Online ISBN: 978-3-319-07953-0
eBook Packages: Computer ScienceComputer Science (R0)