Randomized and Parameterized Algorithms for the Closest String Problem

  • Zhi-Zhong Chen
  • Bin Ma
  • Lusheng Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8486)


Given a set S = {s 1, s 2, …, s n } of strings of equal length L and an integer d, the closest string problem (CSP) requires the computation of a string s of length L such that d(s, s i ) ≤ d for each s i  ∈ S, where d(s, s i ) is the Hamming distance between s and s i . The problem is NP-hard and has been extensively studied in the context of approximation algorithms and parameterized algorithms. Parameterized algorithms provide the most practical solutions to its real-life applications in bioinformatics. In this paper we develop the first randomized parameterized algorithms for CSP. Not only are the randomized algorithms much simpler than their deterministic counterparts, their expected-time complexities are also significantly better than the previously best known (deterministic) algorithms.


Time Complexity Close String Parameterized Algorithm Full Version Input String 
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  1. 1.
    Böcker, S., Jahn, K., Mixtacki, J., Stoye, J.: Computation of median gene clusters. Journal of Computational Biology 16(8), 1085–1099 (2009)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Boucher, C., Brown, D.G.: Detecting motifs in a large data set: Applying probabilistic insights to motif finding. In: Rajasekaran, S. (ed.) BICoB 2009. LNCS, vol. 5462, pp. 139–150. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Ben-Dor, A., Lancia, G., Perone, J., Ravi, R.: Banishing bias from consensus sequences. In: Hein, J., Apostolico, A. (eds.) CPM 1997. LNCS, vol. 1264, pp. 247–261. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Chen, Z.-Z., Ma, B., Wang, L.: A three-string approach to the closest string problem. Journal of Computer and System Sciences 78, 164–178 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    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 Transactions on Computational Biology and Bioinformatics 8(5), 1400–1410 (2011)CrossRefGoogle Scholar
  6. 6.
    Davila, J., Balla, S., Rajasekaran, S.: Space and time efficient algorithms for planted motif search. In: Proc. of the International Conference on Computational Science, pp. 822–829 (2006)Google Scholar
  7. 7.
    Deng, X., Li, G., Li, Z., Ma, B., Wang, L.: Genetic design of drugs without side-effects. SIAM J. Comput. 32(4), 1073–1090 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Dopazo, J., Rodríguez, A., Sáiz, J.C., Sobrino, F.: Design of primers for PCR amplification of highly variable genomes. CABIOS 9, 123–125 (1993)Google Scholar
  9. 9.
    Evans, P.A., Smith, A.D.: Complexity of approximating closest substring problems. In: Proc. of the 14th International Symposium on Foundations of Complexity Theory, pp. 210–221 (2003)Google Scholar
  10. 10.
    Fellows, M.R., Gramm, J., Niedermeier, R.: On the parameterized intractability of motif search problems. Combinatorica 26(2), 141–167 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Frances, M., Litman, A.: On covering problems of codes. Theoret. Comput. Sci. 30, 113–119 (1997)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Gramm, J., Guo, J., Niedermeier, R.: On exact and approximation algorithms for distinguishing substring selection. In: Lingas, A., Nilsson, B.J. (eds.) FCT 2003. LNCS, vol. 2751, pp. 195–209. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Gramm, J., Hüffner, F., Niedermeier, R.: Closest strings, primer design, and motif search. In: Florea, L., et al (eds.), Currents in Computational Molecular Biology. Poster Abstracts of RECOMB 2002, pp. 74–75 (2002)Google Scholar
  14. 14.
    Gramm, J., Niedermeier, R., Rossmanith, P.: Fixed-parameter algorithms for closest string and related problems. Algorithmica 37, 25–42 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Hufsky, F., Kuchenbecker, L., Jahn, K., Stoye, J., Böcker, S.: Swiftly computing center strings. In: Moulton, V., Singh, M. (eds.) WABI 2010. LNCS, vol. 6293, pp. 325–336. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Jiao, Y., Xu, J., Li, M.: On the k-closest substring and k-consensus pattern problems. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 130–144. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Lanctot, K., Li, M., Ma, B., Wang, S., Zhang, L.: Distinguishing string search problems. Inform. and Comput. 185, 41–55 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Li, M., Ma, B., Wang, L.: On the closest string and substring problems. J. ACM 49(2), 157–171 (2002)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Lucas, K., Busch, M., Mösinger, S., Thompson, J.A.: An improved microcomputer program for finding gene- or gene family-specific oligonucleotides suitable as primers for polymerase chain reactions or as probes. CABIOS 7, 525–529 (1991)Google Scholar
  20. 20.
    Ma, B., Sun, X.: More efficient algorithms for closest string and substring problems. SIAM J. Comput. 39(4), 1432–1443 (2010)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Marx, D.: Closest substring problems with small distances. SIAM J. Comput. 38(4), 1382–1410 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Marx, D.: Randomized techniques for parameterized algorithms. In: Thilikos, D.M., Woeginger, G.J. (eds.) IPEC 2012. LNCS, vol. 7535, p. 2. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. 23.
    Mauch, H., Melzer, M.J., Hu, J.S.: Genetic algorithm approach for the closest string problem. In: Proc. of the 2nd IEEE Computer Society Bioinformatics Conference (CSB), pp. 560–561 (2003)Google Scholar
  24. 24.
    Meneses, C.N., Lu, Z., Oliveira, C.A.S., Pardalos, P.M.: Optimal solutions for the closest-string problem via integer programming. INFORMS J. Comput. (2004)Google Scholar
  25. 25.
    Nicolas, F., Rivals, E.: Complexities of the centre and median string problems. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, vol. 2676, pp. 315–327. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  26. 26.
    Proutski, V., Holme, E.C.: Primer master: A new program for the design and analysis of PCR primers. CABIOS 12, 253–255 (1996)Google Scholar
  27. 27.
    Stojanovic, N., Berman, P., Gumucio, D., Hardison, R., Miller, W.: A linear-time algorithm for the 1-mismatch problem. In: Rau-Chaplin, A., Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 1997. LNCS, vol. 1272, pp. 126–135. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  28. 28.
    Wang, L., Dong, L.: Randomized algorithms for motif detection. J. Bioinform. Comput. Biol. 3(5), 1039–1052 (2005)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Wang, L., Zhu, B.: Efficient algorithms for the closest string and distinguishing string selection problems. In: Deng, X., Hopcroft, J.E., Xue, J. (eds.) FAW 2009. LNCS, vol. 5598, pp. 261–270. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  30. 30.
    Wang, Y., Chen, W., Li, X., Cheng, B.: Degenerated primer design to amplify the heavy chain variable region from immunoglobulin cDNA. BMC Bioinform. 7(suppl. 4), S9 (2006)Google Scholar
  31. 31.
    Zhao, R., Zhang, N.: A more efficient closest string algorithm. In: Proc. of the 2nd International Conference on Bioinformatics and Computational Biology (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Zhi-Zhong Chen
    • 1
  • Bin Ma
    • 2
  • Lusheng Wang
    • 3
  1. 1.Division of Information System DesignTokyo Denki UniversityHatoyamaJapan
  2. 2.School of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.Department of Computer ScienceCity University of Hong KongKowloonHong Kong SAR

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