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Lower Bounds for Approximation Schemes for Closest String

Authors Marek Cygan, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Saket Saurabh

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Marek Cygan
Daniel Lokshtanov
Marcin Pilipczuk
Michal Pilipczuk
Saket Saurabh

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Marek Cygan, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Lower Bounds for Approximation Schemes for Closest String. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 12:1-12:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.SWAT.2016.12

Abstract

In the Closest String problem one is given a family S of equal-length strings over some fixed alphabet, and the task is to find a string y that minimizes the maximum Hamming distance between y and a string from S. While polynomial-time approximation schemes (PTASes) for this problem are known for a long time [Li et al.; J. ACM'02], no efficient polynomial-time approximation scheme (EPTAS) has been proposed so far. In this paper, we prove that the existence of an EPTAS for Closest String is in fact unlikely, as it would imply that FPT=W[1], a highly unexpected collapse in the hierarchy of parameterized complexity classes. Our proof also shows that the existence of a PTAS for Closest String with running time f(eps) n^o(1/eps), for any computable function f, would contradict the Exponential Time Hypothesis.
Keywords
  • closest string
  • PTAS
  • efficient PTAS

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References

  1. Alexandr Andoni, Piotr Indyk, and Mihai Pătraşcu. On the optimality of the dimensionality reduction method. In 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), 21-24 October 2006, Berkeley, California, USA, Proceedings, pages 449-458. IEEE Computer Society, 2006. Google Scholar
  2. Cristina Bazgan. Schémas d'approximation et complexité paramétrée. PhD thesis, Université Paris Sud, 1995. In French. Google Scholar
  3. Christina Boucher, Christine Lo, and Daniel Lokshtanov. Consensus Patterns (probably) has no EPTAS. In Algorithms - ESA 2015 - 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings, volume 9294 of Lecture Notes in Computer Science, pages 239-250. Springer, 2015. Full version available at URL: http://www.ii.uib.no/~daniello/papers/ConsensusPatterns.pdf.
  4. Marco Cesati and Luca Trevisan. On the efficiency of polynomial time approximation schemes. Inf. Process. Lett., 64(4):165-171, 1997. Google Scholar
  5. Marek Cygan, Fedor V. Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-319-21275-3,
  6. Jörg Flum and Martin Grohe. Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series. Springer-Verlag, Berlin, 2006. Google Scholar
  7. Jens Gramm, Rolf Niedermeier, and Peter Rossmanith. Fixed-parameter algorithms for Closest String and related problems. Algorithmica, 37(1):25-42, 2003. Google Scholar
  8. Ming Li, Bin Ma, and Lusheng Wang. Finding similar regions in many sequences. J. Comput. Syst. Sci., 65(1):73-96, 2002. Google Scholar
  9. Ming Li, Bin Ma, and Lusheng Wang. On the Closest String and Substring problems. J. ACM, 49(2):157-171, 2002. Google Scholar
  10. Daniel Lokshtanov, Dániel Marx, and Saket Saurabh. Slightly superexponential parameterized problems. In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, January 23-25, 2011, pages 760-776. SIAM, 2011. Google Scholar
  11. Bin Ma and Xiaoming Sun. More efficient algorithms for Closest String and Substring problems. SIAM J. Comput., 39(4):1432-1443, 2009. Google Scholar
  12. Dániel Marx. Closest substring problems with small distances. SIAM J. Comput., 38(4):1382-1410, 2008. Google Scholar
  13. Dániel Marx. Parameterized complexity and approximation algorithms. Comput. J., 51(1):60-78, 2008. Google Scholar
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