pp 1–32 | Cite as

Consensus Strings with Small Maximum Distance and Small Distance Sum

  • Laurent Bulteau
  • Markus L. SchmidEmail author


The parameterised complexity of various 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.


Consensus String Problems Closest String Closest Substring Parameterised Complexity Kernelisation 



We wish to thank the anonymous referees for valuable feedback that improved the readability of this paper.


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Authors and Affiliations

  1. 1.Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEMMarne-la-ValléeFrance
  2. 2.Fachbereich 4 – Abteilung Informatikwissenschaften, Universität TrierTrierGermany

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