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The simplified partial digest problem: Approximation and a graph-theoretic model

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

Abstract

The goal of the simplified partial digest problem (SPDP) is motivated by the reconstruction of the linear structure of a DNA chain with respect to a given nucleotide pattern, based on the multiset of distances between the adjacent patterns (interpoint distances) and the multiset of distances between each pattern and the two unlabeled endpoints of the DNA chain (end distances). We consider optimization versions of the problem, called SPDP-Min and SPDP-Max. The aim of SPDP-Min (SPDP-Max) is to find a DNA linear structure with the same multiset of end distances and the minimum (maximum) number of incorrect (correct) interpoint distances. Results are presented on the worst-case efficiency of approximation algorithms for these problems. We suggest a graph-theoretic model for SPDP-Min and SPDP-Max, which can be used to reduce the search space for an optimal solution in either of these problems. We also present heuristic polynomial time algorithms based on this model. In computational experiments with randomly generated and real-life input data, our best algorithm delivered an optimal solution in 100% of the instances for a number of restriction sites not greater than 50.

Suggested Citation

  • Blazewicz, Jacek & Burke, Edmund K. & Kasprzak, Marta & Kovalev, Alexandr & Kovalyov, Mikhail Y., 2011. "The simplified partial digest problem: Approximation and a graph-theoretic model," European Journal of Operational Research, Elsevier, vol. 208(2), pages 142-152, January.
    • Handle: RePEc:eee:ejores:v:208:y:2011:i:2:p:142-152
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    References listed on IDEAS

    as
    1. Zhang, Ji-Hong & Wu, Ling-Yun & Zhao, Yu-Ying & Zhang, Xiang-Sun, 2007. "An optimization approach to the reconstruction of positional DNA sequencing by hybridization with errors," European Journal of Operational Research, Elsevier, vol. 182(1), pages 413-427, October.
    2. Piotr Łukasiak & Jacek Błażewicz & Maciej Miłostan, 2010. "Some operations research methods for analyzing protein sequences and structures," Annals of Operations Research, Springer, vol. 175(1), pages 9-35, March.
    3. Blazewicz, Jacek & Formanowicz, Piotr & Kasprzak, Marta, 2005. "Selected combinatorial problems of computational biology," European Journal of Operational Research, Elsevier, vol. 161(3), pages 585-597, March.
    4. Jacek Blazewicz & Ceyda Oguz & Aleksandra Swiercz & Jan Weglarz, 2006. "DNA Sequencing by Hybridization via Genetic Search," Operations Research, INFORMS, vol. 54(6), pages 1185-1192, December.
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