On the Closest String via Rank Distance

  • Liviu P. Dinu
  • Alexandru Popa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)


Given a set S of k strings of maximum length n, the goal of the closest substring problem (CSSP) is to find the smallest integer d (and a corresponding string t of length ℓ ≤ n) such that each string s ∈ S has a substring of length ℓ of “distance” at most d to t. The closest string problem (CSP) is a special case of CSSP where ℓ = n. CSP and CSSP arise in many applications in bioinformatics and are extensively studied in the context of Hamming and edit distance. In this paper we consider a recently introduced distance measure, namely the rank distance. First, we show that the CSP and CSSP via rank distance are NP-hard. Then, we present a polynomial time k-approximation algorithm for the CSP problem. Finally, we give a parametrized algorithm for the CSP (the parameter is the number of input strings) if the alphabet is binary and each string has the same number of 0’s and 1’s.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Liviu P. Dinu
    • 1
  • Alexandru Popa
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  2. 2.Department of Communications & NetworkingAalto University School of Electrical EngineeringAaltoFinland

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