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.
| Original language | English |
|---|---|
| Pages (from-to) | 371-374 |
| Number of pages | 4 |
| Journal | Information Processing Letters |
| Volume | 113 |
| Issue number | 10-11 |
| DOIs | |
| State | Published - 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.
Keywords
- Combinatorial problems
- Computational complexity
- Consensus
- Hamming distance Swap Reversal