Minimum Multicolored Subgraph Problem in Multiplex PCR Primer Set Selection and Population Haplotyping

  • M. T. Hajiaghayi
  • K. Jain
  • L. C. Lau
  • I. I. Măndoiu
  • A. Russell
  • V. V. Vazirani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3992)

Abstract

In this paper we consider the minimum weight multicolored subgraph problem (MWMCSP), which is a common generalization of minimum cost multiplex PCR primer set selection and maximum likelihood population haplotyping. In this problem one is given an undirected graph G with non-negative vertex weights and a color function that assigns to each edge one or more of n given colors, and the goal is to find a minimum weight set of vertices inducing edges of all n colors. We obtain improved approximation algorithms and hardness results for MWMCSP and its variant in which the goal is to find a minimum number of vertices inducing edges of at least k colors for a given integer kn.

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References

  1. 1.
    Fernandes, R., Skiena, S.: Microarray synthesis through multiple-use PCR primer design. Bioinformatics 18, S128–S135 (2002)Google Scholar
  2. 2.
    Clark, A.: The role of haplotypes in candidate gene studies. Genet. Epid. 27, 321–333 (2004)CrossRefGoogle Scholar
  3. 3.
    Bonizzoni, P., Vedova, G.D., Dondi, R., Li, J.: The haplotyping problem: An overview of computational models and solutions. Journal of Computer Science and Technology 18, 675–688 (2003)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Halldorsson, B., Bafna, V., Edwards, N., Lippert, R., Yooseph, S., Istrail, S.: A survey of computational methods for determining haplotypes. In: Proc. of the DIMACS/RECOMB Satellite Workshop on Computational Methods for SNPs and Haplotype Inference, pp. 26–47 (2004)Google Scholar
  5. 5.
    Niu, T.: Algorithms for inferring haplotypes. Genet. Epid. 27, 334–347 (2004)CrossRefGoogle Scholar
  6. 6.
    Halperin, E., Hazan, E.: HAPLOFREQ - estimating haplotype frequencies efficiently. In: Proc. 9th Annual International Conference on Research in Computational Molecular Biology, pp. 553–568 (2005)Google Scholar
  7. 7.
    Gusfield, D.: Haplotyping by pure parsimony. In: Proc. 14th Annual Symp. on Combinatorial Pattern Matching, pp. 144–155 (2003)Google Scholar
  8. 8.
    Lancia, G., Pinotti, C., Rizzi, R.: Haplotyping populations: complexity and approximations. Technical Report DIT-02-0080, University of Trento (2002)Google Scholar
  9. 9.
    Wang, L., Xu, Y.: Haplotype inference by maximum parsimony. Bioinformatics 19, 1773–1780 (2003)CrossRefGoogle Scholar
  10. 10.
    Brown, D., Harrower, I.: A New Integer Programming Formulation for the Pure Parsimony Problem in Haplotype Analysis. In: Proc. 4th International Workshop on Algorithms in Bioinformatics, pp. 254–265 (2004)Google Scholar
  11. 11.
    Lancia, G., Pinotti, M., Rizzi, R.: Haplotyping populations by pure parsimony: Complexity of exact and approximation algorithms. INFORMS Journal on Computing 16, 348–359 (2004)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Konwar, K., Măndoiu, I., Russell, A., Shvartsman, A.: Improved algorithms for multiplex PCR primer set selection with amplification length constraints. In: Proc. 3rd Asia-Pacific Bioinformatics Conference, pp. 41–50 (2005)Google Scholar
  13. 13.
    Hassin, R., Segev, D.: The set cover with pairs problem. In: Proc. 25th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, pp. 164–176 (2005)Google Scholar
  14. 14.
    Huang, Y.T., Chao, K.M., Chen, T.: An approximation algorithm for haplotype inference by maximum parsimony. Journal of Computational Biology 12, 1261–1274 (2005)CrossRefGoogle Scholar
  15. 15.
    Slavik, P.: Improved performance of the greedy algorithm for partial cover. Information Processing Letters 64, 251–254 (1997)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Gandhi, R., Khuller, S., Srinivasan, A.: Approximation algorithms for partial covering problems. Journal of Algorithms 53, 55–84 (2004)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Feige, U., Kortsarz, G., Peleg, D.: The dense k-subgraph problem. Algorithmica 29(3), 410–421 (2001)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Khot, S.: Ruling out PTAS for graph min-bisection, densest subgraph and bipartite clique. In: Proc. 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 136–145 (2004)Google Scholar
  19. 19.
    Feige, U.: Relations between average case complexity and approximation complexity. In: Proc. 34th Annual ACM Symposium on Theory of Computing, pp. 534–543 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. T. Hajiaghayi
    • 1
  • K. Jain
    • 2
  • L. C. Lau
    • 3
  • I. I. Măndoiu
    • 4
  • A. Russell
    • 4
  • V. V. Vazirani
    • 5
  1. 1.Laboratory for Computer ScienceMITUSA
  2. 2.Microsoft ResearchUSA
  3. 3.Department of Computer ScienceUniversity of TorontoCanada
  4. 4.CSE DepartmentUniversity of ConnecticutUSA
  5. 5.College of ComputingGeorgia Institute of TechnologyUSA

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