Abstract
Graph-theoretic models have come to the forefront as some of the most powerful and practical methods for sequence assembly. Simultaneously, the computational hardness of the underlying graph algorithms has remained open. Here we present two theoretical results about the complexity of these models for sequence assembly. In the first part, we show sequence assembly to be NP-hard under two different models: string graphs and de Bruijn graphs. Together with an earlier result on the NP-hardness of overlap graphs, this demonstrates that all of the popular graph-theoretic sequence assembly paradigms are NP-hard. In our second result, we give the first, to our knowledge, optimal polynomial time algorithm for genome assembly that explicitly models the double-strandedness of DNA. We solve the Chinese Postman Problem on bidirected graphs using bidirected flow techniques and show to how to use it to find the shortest double-stranded DNA sequence which contains a given set of k-long words. This algorithm has applications to sequencing by hybridization and short read assembly.
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
Edmonds, J.: An introduction to matching. Notes of engineering summer conference, University of Michigan, Ann Arbor (1967)
Edmonds, J., Johnson, E.L.: Matching, Euler tours, and the Chinese postman. Mathemetical Programming 5, 88–124 (1973)
Gabow, H.N.: An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems. In: STOC, pp. 448–456 (1983)
Gallant, J., Maier, D., Storer, J.A.: On finding minimal length superstrings. J. Comput. Syst. Sci. 20(1), 50–58 (1980)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)
Kececioglu, J.D., Myers, E.W.: Combinatiorial algorithms for DNA sequence assembly. Algorithmica 13(1/2), 7–51 (1995)
Kececioglu, J.D., Sankoff, D.: Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement. Algorithmica 13(1/2), 180–210 (1995)
Kececioglu, J.D.: Exact and approximation algorithms for DNA sequence reconstruction. PhD thesis, Tucson, AZ, USA (1992)
Myers, E.W.: Toward simplifying and accurately formulating fragment assembly. Journal of Computational Biology 2(2), 275–290 (1995)
Myers, E.W.: The fragment assembly string graph. In: ECCB/JBI, p. 85 (2005)
Pevzner, P.A.: 1-Tuple DNA sequencing: computer analysis. J. Biomol. Struct. Dyn. 7(1), 63–73 (1989)
Pevzner, P.A., Tang, H., Waterman, M.S.: An Eulerian path approach to DNA fragment assembly. In: Proceedings of the National Academy of Sciences, vol. 98, pp. 9748–9753 (2001)
Pevzner, P.A., Tang, H., Tesler, G.: De novo repeat classification and fragment assembly. In: RECOMB, pp. 213–222 (2004)
Schrijver, A.: Combinatorial Optimization, vol. A. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Medvedev, P., Georgiou, K., Myers, G., Brudno, M. (2007). Computability of Models for Sequence Assembly. In: Giancarlo, R., Hannenhalli, S. (eds) Algorithms in Bioinformatics. WABI 2007. Lecture Notes in Computer Science(), vol 4645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74126-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-74126-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74125-1
Online ISBN: 978-3-540-74126-8
eBook Packages: Computer ScienceComputer Science (R0)