Skip to main content
SpringerLink
Log in

The Parameterized Complexity of the Shared Center Problem

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Recently, the shared center (SC) problem has been proposed as a mathematical model for inferring the allele-sharing status of a given set of individuals using a database of confirmed haplotypes as reference. The problem was proved to be NP-complete and a ratio-2 polynomial-time approximation algorithm was designed for its minimization version (called the closest shared center (CSC) problem). In this paper, we consider the parameterized complexity of the SC problem. First, we show that the SC problem is W[1]-hard with parameters d and n, where d and n are the radius and the number of (diseased or normal) individuals in the input, respectively. Then, we present two asymptotically optimal parameterized algorithms for the problem and apply them to linkage analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Cai, Z., Sabaa, H., Wang, Y., Goebel, R., Wang, Z., Xu, J., Stothard, P., Lin, G.: Most parsimonious haplotype allele sharing determination. BMC Bioinform. 10, 115 (2009)

    Article  Google Scholar 

  2. Chen, Z.-Z., Wang, L.: Fast exact algorithms for the closest string and substring problems with application to the planted (L,d)-motif model. IEEE/ACM Trans. Comput. Biol. Bioinform. 8(5), 1400–1410 (2011)

    Article  Google Scholar 

  3. Chen, Z.-Z., Ma, B., Wang, L.: A three-string approach to the closest string problem. J. Comput. Syst. Sci. 78, 164–178 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Doi, K., Li, J., Jiang, T.: Minimum recombinant haplotype configuration on tree pedigrees. In: Proceedings of Workshop on Algorithms in Bioinformatics (WABI), pp. 339–353 (2003)

    Chapter  Google Scholar 

  5. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Monogr. Comput. Sci. Springer, New York (1999)

    Book  Google Scholar 

  6. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006)

    Google Scholar 

  7. Gramm, J., Niedermeier, R., Rossmanith, P.: Fixed-parameter algorithms for closest string and related problems. Algorithmica 37, 25–42 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Impagliazzo, R., Paturi, R.: The Complexity of k-SAT. In: Proceedings of the 14th IEEE Conference on Computational Complexity, pp. 237–240 (1999)

    Google Scholar 

  9. Li, J., Jiang, T.: An exact solution for finding minimum recombinant haplotype configurations on pedigrees with missing data by integer linear programming. In: Proceedings of Symposium on Computational Molecular Biology (RECOMB), pp. 20–29 (2004)

    Google Scholar 

  10. Li, J., Jiang, T.: Computing the minimum recombinant haplotype configuration from incomplete genotype data on a pedigree by integer linear programming. J. Comput. Biol. 12(6), 719–739 (2005)

    Article  MATH  Google Scholar 

  11. Lin, G., Wang, Z., Wang, L., Lau, Y.-L., Yang, W.: Identification of linked regions using high-density SNP genotype data in linkage analysis. Bioinformatics 24(1), 86–93 (2008)

    Article  Google Scholar 

  12. Ma, W., Yang, Y., Chen, Z.-Z., Wang, L.: Mutation region detection for closely related individuals without a known pedigree. IEEE/ACM Trans. Comput. Biol. Bioinform. 9(2), 499–510 (2012)

    Article  Google Scholar 

  13. Ma, B., Sun, X.: More efficient algorithms for closest string and substring problems. SIAM J. Comput. 39, 1432–1443 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Marx, D.: Closest substring problems with small distances. SIAM J. Comput. 38, 1382–1410 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Qian, D., Beckmann, L.: Minimum recombinant haplotyping in pedigrees. Am. J. Hum. Genet. 70, 1434–1445 (2002)

    Article  Google Scholar 

  16. Tapadar, P., Ghosh, S., Majumder, P.P.: Haplotyping in pedigrees via a genetic algorithm. Hum. Hered. 43, 56 (1999)

    Google Scholar 

  17. Wang, L., Zhu, B.: Efficient algorithms for the closest string and distinguishing string selection problems. In: Proceedings of the 3rd International Workshop on Frontiers in Algorithmics, pp. 261–270 (2009)

    Chapter  Google Scholar 

  18. Xiao, J., Liu, L., Xia, L., Jiang, T.: Fast elimination of redundant linear equations and reconstruction of recombination-free Mendelian inheritance on a pedigree. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 655–664 (2007)

    Google Scholar 

  19. Zhang, K., Sun, F., Zhao, H.: Haplore: a program for haplotype reconstruction in general pedigrees without recombination. Bioinformatics 21, 90–103 (2005)

    Article  Google Scholar 

  20. Zhao, R., Zhang, N.: A more efficient closest string algorithm. In: Proceedings of the 2nd International Conference on Bioinformatics and Computational Biology (BICoB), pp. 210–215 (2010)

    Google Scholar 

Download references

Acknowledgements

We thank the referees for very helpful comments. This work is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 121608).

Author information

Authors and Affiliations

  1. Division of Information System Design, Tokyo Denki University, Ishizaka, Hatoyama, Hiki, Saitama, 359-0394, Japan

    Zhi-Zhong Chen

  2. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Wenji Ma & Lusheng Wang

Authors
  1. Zhi-Zhong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenji Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lusheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Zhong Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, ZZ., Ma, W. & Wang, L. The Parameterized Complexity of the Shared Center Problem. Algorithmica 69, 269–293 (2014). https://doi.org/10.1007/s00453-012-9730-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-012-9730-7

Keywords

Search

Navigation