Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T10:09:48.713Z Has data issue: false hasContentIssue false
  • English
  • Français

Combinatorial optimization in DNA mapping — a computational threadof the Simplified Partial Digest Problem

Published online by Cambridge University Press:  08 April 2006

Jacek Blazewicz  and
Marta Kasprzak
Jacek Blazewicz
Affiliation:
Institute of Computing Science, Poznan University of Technology, Piotrowo 3A, 60–965 Poznan, Poland; jblazewicz@cs.put.poznan.pl Institute of Bioorganic Chemistry, Polish Academy of Sciences, Poznan, Poland; marta@cs.put.poznan.pl
Marta Kasprzak
Affiliation:
Institute of Computing Science, Poznan University of Technology, Piotrowo 3A, 60–965 Poznan, Poland; jblazewicz@cs.put.poznan.pl Institute of Bioorganic Chemistry, Polish Academy of Sciences, Poznan, Poland; marta@cs.put.poznan.pl
Get access

Abstract

In the paper, the problem of the genome mapping of DNA molecules, is presented. In particular, the new approach — the Simplified Partial Digest Problem (SPDP), is analyzed. This approach, although easy in laboratory implementation and robust with respect to measurement errors, when formulated in terms of a combinatorial search problem, is proved to be strongly NP-hard for the general error-free case. For a subproblem of the SPDP, a simple O(nlogn)-time algorithm is given, where n is a number of restriction sites.

Keywords

Combinatorial optimizationDNA restriction mappingpartial digestcomputational complexity.
Type
Research Article
Information
RAIRO - Operations Research , Volume 39 , Issue 4 , October 2005 , pp. 227 - 241
Copyright
© EDP Sciences, 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

S. Benzer, On the topology of the genetic fine structure, in Proceedings of the National Academy of Sciences of the USA 45 (1959) 1607–1620.
Blazewicz, J., Formanowicz, P., Kasprzak, M., Jaroszewski, M. and Markiewicz, W.T., Construction of DNA restriction maps based on a simplified experiment. Bioinformatics 17 (2001) 398–404. CrossRef
Blazewicz, J. and Jaroszewski, M., New algorithm for the Simplified Partial Digest Problem. Lect. Notes Bioinformatics 2812 (2003) 95–110.
Blazewicz, J. and Kasprzak, M., Complexity of DNA sequencing by hybridization. Theoret. Comput. Sci. 290 (2003) 1459–1473. CrossRef
Cieliebak, M. and Eidenbenz, S., Measurement errors make the partial digest problem NP-hard. Lect. Notes Comput. Sci. 2976 (2004) 379–390. CrossRef
Cieliebak, M., Eidenbenz, S. and Penna, P., Noisy data make the partial digest problem NP-hard. Lect. Notes Bioinformatics 2812 (2003) 111–123.
G.B. Fogel and D.W. Corne, eds. Evolutionary Computations in Bioinformatics. Morgan Kaufman, Boston (2003).
M.R. Garey and D.S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco (1979).
Goldstein, L. and Waterman, M.S., Mapping DNA by stochastic relaxation. Adv. Appl. Math. 8 (1987) 194–207. CrossRef
D.S. Johnson, The NP-completeness column: an ongoing guide. J. Algorithms (1985) 6 291–305.
R.M. Karp and R. Shamir, Algorithms for optical mapping, in Proceedings of the Second International Conference on Computational Biology (RECOMB), New York, (1998) 117–124.
M. Kasprzak, Computational complexity of the Simplified Partial Digest Problem, in 05441 Abstracts Collection — Managing and Mining Genome Information: Frontiers in Bioinformatics, edited by J. Blazewicz, J.Ch. Freytag and M. Vingron. IBFI, Dagstuhl (2005).
Newberg, L. and Naor, D., A lower bound on the number of solutions of the probed partial digest problem. Adv. Appl. Math. 14 (1993) 172–183. CrossRef
Pandurangan, G. and Ramesh, H., The restriction mapping problem revisited. J. Comput. Syst. Sci. 65 (2002) 526–544. CrossRef
P.A. Pevzner, Computational Molecular Biology: An Algorithmic Approach. MIT Press, Cambridge (2000).
Schmitt, W. and Waterman, M.S., Multiple solutions of DNA restriction mapping problem. Adv. Appl. Math. 12 (1991) 412–427. CrossRef
Schwartz, D.C., Li, X., Hernandez, L.I., Ramnarain, S.P., Huff, E.J. and Wang, Y.K., Ordered restriction maps of Saccharomyces cerevisiac chromosomes constructed by optical mapping. Science 262 (1993) 110–114. CrossRef
J. Setubal and J. Meidanis, Introduction to Computational Biology. PWS Publishing Company, Boston (1997).
S.S. Skiena, Geometric reconstruction problems, in Handbook of Discrete and Computational Geometry edited by J.E. Goodman and J. O'Rourke. CRC Press, Boca Raton (1997), 481–490.
S.S. Skiena, W.D. Smith and P. Lemke, Reconstructing sets from interpoint distances in Proceedings of Sixth ACM Symposium on Computational Geometry (1990) 332–339.
Skiena, S.S. and Sundaram, G., A partial digest approach to restriction site mapping. Bull. Math. Biology 56 (1994) 275–294. CrossRef
M.S. Waterman, Introduction to Computational Biology. Maps, Sequences and Genomes, Chapman and Hall: London (1995).