Consensus Strings with Small Maximum Distance and Small Distance Sum

Authors Laurent Bulteau, Markus L. Schmid

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Author Details

Laurent Bulteau
  • Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, F-77454, Marne-la-Vallée, France
Markus L. Schmid
  • Fachbereich 4 - Abteilung Informatikwissenschaften, Universität Trier, 54286 Trier, Germany

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Laurent Bulteau and Markus L. Schmid. Consensus Strings with Small Maximum Distance and Small Distance Sum. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The parameterised complexity of consensus string problems (Closest String, Closest Substring, Closest String with Outliers) is investigated in a more general setting, i. e., with a bound on the maximum Hamming distance and a bound on the sum of Hamming distances between solution and input strings. We completely settle the parameterised complexity of these generalised variants of Closest String and Closest Substring, and partly for Closest String with Outliers; in addition, we answer some open questions from the literature regarding the classical problem variants with only one distance bound. Finally, we investigate the question of polynomial kernels and respective lower bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → W hierarchy
  • Consensus String Problems
  • Closest String
  • Closest Substring
  • Parameterised Complexity
  • Kernelisation


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  1. A. Amir, G. M. Landau, J. C. Na, H. Park, K. Park, and J. S. Sim. Efficient algorithms for consensus string problems minimizing both distance sum and radius. Theoretical Computer Science, 412:5239-5246, 2011. Google Scholar
  2. M. Basavaraju, F. Panolan, A. Rai, M. S. Ramanujan, and S. Saurabh. On the kernelization complexity of string problems. In Proc. 20th International Conference on Computing and Combinatorics, COCOON 2014, volume 8591 of LNCS, pages 141-153, 2014. Google Scholar
  3. A. Ben-Dor, G. Lancia, R. Ravi, and J. Perone. Banishing bias from consensus sequences. In Proc. 8th Annual Symposium on Combinatorial Pattern Matching, CPM 1997, volume 1264 of LNCS, pages 247-261, 1997. Google Scholar
  4. H. L. Bodlaender, B. M. P. Jansen, and S. Kratsch. Kernelization lower bounds by cross-composition. SIAM Journal of Discrete Mathematics, 28(1):277-305, 2014. Google Scholar
  5. C. Boucher and B. Ma. Closest string with outliers. BMC Bioinformatics, 12:S55, 2011. Google Scholar
  6. L. Bulteau, F. Hüffner, C. Komusiewicz, and R. Niedermeier. Multivariate algorithmics for NP-hard string problems. Bulletin of the EATCS, 114:31-73, 2014. Google Scholar
  7. M. Cygan, F. Fomin, \L. Kowalik, D. Lokshtanov, D. Marx, M. Pilipczuk, M. Pilipczuk, and S. Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  8. X. Deng, G. Li, Z. Li, B. Ma, and L. Wang. Genetic design of drugs without side-effects. SIAM Journal of Computing, 32(4):1073-1090, 2003. Google Scholar
  9. J. Dopazo, A. Rodríguez, J. Sáiz, and F. Sobrino. Design of primers for PCR amplification of highly variable genomes. Computer Applications in the Biosciences, 9(2):123-125, 1993. Google Scholar
  10. R. G. Downey and M. R. Fellows. Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, 2013. Google Scholar
  11. Rodney G Downey and Michael Ralph Fellows. Parameterized complexity. Springer Science &Business Media, 2012. Google Scholar
  12. P. A. Evans, A. Smith, and H. T. Wareham. The parameterized complexity of p-center approximate substring problems. Technical Report TR01-149, Faculty of Computer Science, University of New Brunswick, Canada, 2001. Google Scholar
  13. P. A. Evans, A. D. Smith, and H. T. Wareham. On the complexity of finding common approximate substrings. Theoretical Computer Science, 306:407-430, 2003. Google Scholar
  14. M. R. Fellows, J. Gramm, and R. Niedermeier. On the parameterized intractability of motif search problems. Combinatorica, 26:141-167, 2006. Google Scholar
  15. J. Flum and M. Grohe. Parameterized Complexity Theory. Springer, 2006. Google Scholar
  16. M. Frances and A. Litman. On covering problems of codes. Theory of Computing Systems, 30:113-119, 1997. Google Scholar
  17. J. Gramm, R. Niedermeier, and P. Rossmanith. Fixed-parameter algorithms for closest string and related problems. Algorithmica, 37:25-42, 2003. Google Scholar
  18. J. K. Lanctot, M. Li, B. Ma, S. Wang, and L. Zhang. Distinguishing string selection problems. Information and Computation, 185:41-55, 2003. Google Scholar
  19. K. Lucas, M. Busch, S. Mössinger, and J. A. Thompson. An improved microcomputer program for finding gene- or gene family-specific oligonucleotides suitable as primers for polymerase chain reactions or as probes. Computer Applications in the Biosciences, 7(4):525-529, 1991. Google Scholar
  20. D. Marx. Closest substring problems with small distances. SIAM Journal on Computing, 38:1382-1410, 2008. Google Scholar
  21. G. Pavesi, G. Mauri, and G. Pesole. An algorithm for finding signals of unknown length in DNA sequences. Bioinformatics, 17:S207-S214, 2001. Google Scholar
  22. P. Pevzner and S. Sze. Combinatorial approaches to finding subtle signals in DNA strings. In Proceedings of the 8th International Conference on Intelligent Systems for Molecular Biology, ISMB 2000, pages 269-278, 2000. Google Scholar
  23. V. Proutski and E. C. Holmes. Primer master: a new program for the design and analysis of PCR primers. Computer Applications in the Biosciences, 12(3):253-255, 1996. Google Scholar
  24. Markus L. Schmid. Finding consensus strings with small length difference between input and solution strings. ACM Transactions on Computation Theory, 9(3):13:1-13:18, 2017. Google Scholar
  25. M. Tompa, N. Li, T. L. Bailey, G. M. Church, B. De Moor, E. Eskin, A. V. Favorov, M. C. Frith, Y. Fu, W. J. Kent, V. J. Makeev, A. A. Mironov, W. S. Noble, G. Pavesi, G. Pesole, M. Régnier, N. Simonis, S. Sinha, G. Thijs, J. van Helden, M. Vandenbogaert, Z. Weng, C. Workman, C. Ye, and Z. Zhu. Assessing computational tools for the discovery of transcription factor binding sites. Nature Biotechnology, 23(1):137-144, 2005. Google Scholar
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