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Randomized Fixed-Parameter Algorithms for the Closest String Problem

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Abstract

Given a set \(S = \{s_1, s_2, \ldots , s_n\}\) of strings of equal length \(L\) and an integer \(d\), the closest string problem (CSP) requires the computation of a string \(s\) of length \(L\) such that \(d(s, s_i) \le d\) for each \(s_i \in S\), where \(d(s, s_i)\) is the Hamming distance between \(s\) and \(s_i\). The problem is NP-hard and has been extensively studied in the context of approximation algorithms and fixed-parameter algorithms. Fixed-parameter algorithms provide the most practical solutions to its real-life applications in bioinformatics. In this paper we develop the first randomized fixed-parameter algorithms for CSP. Not only are the randomized algorithms much simpler than their deterministic counterparts, their time complexities are also significantly better than the previously best known (deterministic) algorithms.

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Acknowledgments

We thank the anonymous referees for very helpful comments. Zhi-Zhong Chen was supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan, under Grant No. 24500023. Bin Ma was supported in part by Natural Sciences and Engineering Research Council of Canada (RGPIN 238748). Lusheng Wang was supported by a GRF grant from Hong Kong SAR government Project No. [CityU 123013] and a grant from National Foundation of China Project No. [61373048].

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Authors and Affiliations

  1. Division of Information System Design, Tokyo Denki University, Ishizaka, Hatoyama, Hiki, Saitama, 350-0394, Japan

    Zhi-Zhong Chen

  2. School of Computer Science, University of Waterloo, 200 University Ave. W, Waterloo, ON, N2L3G1, Canada

    Bin Ma

  3. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR

    Lusheng Wang

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  1. Zhi-Zhong Chen
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  3. Lusheng Wang
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Correspondence to Zhi-Zhong Chen.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 25th Annual Symposium on Combinatorial Pattern Matching, 2014.

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Chen, ZZ., Ma, B. & Wang, L. Randomized Fixed-Parameter Algorithms for the Closest String Problem. Algorithmica 74, 466–484 (2016). https://doi.org/10.1007/s00453-014-9952-y

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