On the hardness of the Consensus String problem

Amihood Amir; Haim Paryenty; Liam Roditty

doi:10.1016/j.ipl.2013.02.016

On the hardness of the Consensus String problem

Amihood Amir, Haim Paryenty, Liam Roditty

Department of Computer Science

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

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,⋯, s_k} 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 language	English
Pages (from-to)	371-374
Number of pages	4
Journal	Information Processing Letters
Volume	113
Issue number	10-11
DOIs	https://doi.org/10.1016/j.ipl.2013.02.016
State	Published - 2013

Keywords

Combinatorial problems
Computational complexity
Consensus
Hamming distance Swap Reversal

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2013.02.016

Cite this

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title = "On the hardness of the Consensus String problem",

abstract = "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.",

keywords = "Combinatorial problems, Computational complexity, Consensus, Hamming distance Swap Reversal",

author = "Amihood Amir and Haim Paryenty and Liam Roditty",

note = "Funding Information: University, Ramat-Gan 52900, Israel. Tel.: +972 3 531 8770. E-mail addresses: [email protected] (A. Amir), [email protected] (H. Paryenty), [email protected] (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{\textquoteright}s Fellowship. This work is part of Haim Paryenty{\textquoteright}s Ph.D. dissertation. 3 Tel.: +972 3 531 7874.",

year = "2013",

doi = "10.1016/j.ipl.2013.02.016",

language = "الإنجليزيّة",

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AU - Amir, Amihood

AU - Paryenty, Haim

AU - Roditty, Liam

N1 - Funding Information: University, Ramat-Gan 52900, Israel. Tel.: +972 3 531 8770. E-mail addresses: [email protected] (A. Amir), [email protected] (H. Paryenty), [email protected] (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.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Combinatorial problems

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On the hardness of the Consensus String problem

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Keywords

All Science Journal Classification (ASJC) codes

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