On the approximability of the Simplified Partial Digest Problem

  • Authors:

  • Jacek Blazewicz;Edmund K. Burke;Marta Kasprzak;Alexandr Kovalev;Mikhail Y. Kovalyov

  • Affiliations:

  • Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland and Institute of Bioorganic Chemistry, Polish Academy of Sciences, Z. Noskowskiego 12/14, 61-704 ...;School of Computer Science, University of Nottingham, Jubilee Campus, Nottingham NG8 1BB, UK;Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland and Institute of Bioorganic Chemistry, Polish Academy of Sciences, Z. Noskowskiego 12/14, 61-704 ...;Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland;Belarusian State University, Nezavisimosti 4, 220030 Minsk, Belarus and United Institute of Informatics Problems, National Academy of Sciences of Belarus, Surganova 6, 220012 Minsk, Belarus

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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Abstract

In this paper, we analyse the computational complexity of an optimization version of the Simplified Partial Digest Problem (SPDP), which is a mathematical model for DNA mapping based on the results of a simplified partial digest experiment. We prove that recognizing 46.16% of the elements of the DNA map in the error-free simplified partial digest experiment is NP-hard in the strong sense. This implies that the problem of maximizing the number of correct elements of the DNA map in the error-free simplified partial digest experiment is pseudopolynomially non-approximable with the approximation ratio @r=136.