Journal of Combinatorial Optimization

, Volume 13, Issue 2, pp 179-188

First online:

RNA multiple structural alignment with longest common subsequences

  • Sergey BeregAffiliated withDepartment of Computer Science, University of Texas at Dallas
  • , Marcin KubicaAffiliated withInstitute of Informatics, Warsaw University
  • , Tomasz WaleńAffiliated withInstitute of Informatics, Warsaw University
  • , Binhai ZhuAffiliated withDepartment of Computer Science, Montana State University Email author 

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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(n 2) 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(n 5) 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 alignment Longest common subsequence Dynamic programming