Journal of Combinatorial Optimization

, Volume 13, Issue 2, pp 179–188

RNA multiple structural alignment with longest common subsequences


  • Sergey Bereg
    • Department of Computer ScienceUniversity of Texas at Dallas
  • Marcin Kubica
    • Institute of InformaticsWarsaw University
  • Tomasz Waleń
    • Institute of InformaticsWarsaw University
    • Department of Computer ScienceMontana State University

DOI: 10.1007/s10878-006-9020-x

Cite this article as:
Bereg, S., Kubica, M., Waleń, T. et al. J Comb Optim (2007) 13: 179. doi:10.1007/s10878-006-9020-x


In this paper, we present a new model for RNA multiple sequence structural alignment based on the longest common subsequence. We consider both the off-line and on-line cases. For the off-line case, i.e., when the longest common subsequence is given as a linear graph with n vertices, we first present a polynomial O(n2) time algorithm to compute its maximum nested loop. We then consider a slightly different problem—the Maximum Loop Chain problem and present an algorithm which runs in O(n5) time. For the on-line case, i.e., given m RNA sequences of lengths n, compute the longest common subsequence of them such that this subsequence either induces a maximum nested loop or the maximum number of matches, we present efficient algorithms using dynamic programming when m is small.


RNA multiple structure alignmentLongest common subsequenceDynamic programming
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© Springer Science+Business Media, LLC 2006