On the hardness of the Consensus String problem

Amihood Amir, Haim Paryenty, Liam Roditty

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10 Scopus citations


Finding the consensus of a given set of strings is a hard and challenging problem. The problem is formally defined as follows: given a set of strings S={s1,⋯, sk} and a constant d, find, if it exists, a string s* such that the distance of s* from each of the strings does not exceed d. This problem has many applications. Two examples are: In biology, it may be used to seek a common ancestor to given sections of DNA. In web searching it may be used as a clustering aid. The stringology community researched this problem under the Hamming distance. In that metric the problem is NP-hard. A lot of work has been also done in the Euclidean metric. In this paper we consider the Consensus problem under other string metrics. We show that this problem is NP-hard for the swap metric and APX-hard for the reversal metric.

Original languageEnglish
Pages (from-to)371-374
Number of pages4
JournalInformation Processing Letters
Issue number10-11
StatePublished - 2013

Bibliographical note

Funding Information:
University, Ramat-Gan 52900, Israel. Tel.: +972 3 531 8770. E-mail addresses: amir@cs.biu.ac.il (A. Amir), haimpa@gmail.com (H. Paryenty), liamr@macs.biu.ac.il (L. Roditty). 1 Partly supported by NSF grant CCR-09-04581 and ISF grant 347/09. 2 Partly supported by a Bar-Ilan University President’s Fellowship. This work is part of Haim Paryenty’s Ph.D. dissertation. 3 Tel.: +972 3 531 7874.


  • Combinatorial problems
  • Computational complexity
  • Consensus
  • Hamming distance Swap Reversal


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