IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v208y2011i2p142-152.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00542-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    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 & Kasprzak, Marta & Kierzynka, Michal & Frohmberg, Wojciech & Swiercz, Aleksandra & Wojciechowski, Pawel & Zurkowski, Piotr, 2018. "Graph algorithms for DNA sequencing – origins, current models and the future," European Journal of Operational Research, Elsevier, vol. 264(3), pages 799-812.
    4. Almeida, Maria Teresa & Carvalho, Filipa D., 2014. "An analytical comparison of the LP relaxations of integer models for the k-club problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 489-498.
    5. Butenko, S. & Wilhelm, W.E., 2006. "Clique-detection models in computational biochemistry and genomics," European Journal of Operational Research, Elsevier, vol. 173(1), pages 1-17, August.
    6. Carvalho, Filipa D. & Almeida, M. Teresa, 2011. "Upper bounds and heuristics for the 2-club problem," European Journal of Operational Research, Elsevier, vol. 210(3), pages 489-494, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:208:y:2011:i:2:p:142-152. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.