RNA multiple structural alignment with longest common subsequences
 Sergey Bereg,
 Marcin Kubica,
 Tomasz Waleń,
 Binhai Zhu
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Abstract
In this paper, we present a new model for RNA multiple sequence structural alignment based on the longest common subsequence. We consider both the offline and online cases. For the offline 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 online 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.
 Chin FYL, De Santis A, Ferrara AL, Ho NL, Kim SK (2004) A simple algorithm for the constrained sequence problems. Inform Proc Lett 90(4):175–179
 Cormen T, Leiserson C, Rivest R, Stein C (2001) Introduction to Algorithms, 2nd edn, MIT Press
 Dayhoff M (1965) Computer aids to protein sequence determination. J Theoret Biol 8(1):97–112 CrossRef
 Dayhoff M (1969) Computer analysis of protein evolution. Sci Am 221(1):86–95 CrossRef
 Davydov E, Batzoglu S (2004) A computational model for RNA multiple structural alignment. In: Proc. 15th Ann. Symp. Combinatorial Pattern Matching, LNCS 3109, pp 254–269
 Deng X, Li G, Li Z, Ma B, Wang L (2002) A PTAS for distinguishing (sub)string selection. In: Proc. ICALP’02, pp 740–751
 Eddy SR (2001) Noncoding RNA genes and the modern RNA world. Nat Rev Genet 2:919–929 CrossRef
 Goldman D, Istrail S, Papadimitriou C (1999) Algorithmic aspects of protein structure similarity. In: Proc. 40th Ann. Symp. Foundations of Computer Science (FOCS’99), pp 512–522
 Greenberg RI (2003) Bounds on the Number of the Longest Common Subsequence Problem. CoRR cs.DM/0301030
 Hirschberg D (1975) The longest common subsequence problem. PhD Thesis, Princeton University
 Hsu WJ, Du MW (1984) Computing a longest common subsequence for a set of strings. BIT 24:45–59 CrossRef
 Jiang T, Li M (1995) On the approximation of shortest common supersequences and longest common subsequences. SIAM J Comput 24(5):1122–1139 CrossRef
 Kubica M, Rizzi R, Vialette S, Walen T (2006) Approximation of RNA multiple structural alignment. In: Proc. 17th Ann Symp Combinatorial Pattern Matching, LNCS 4009, pp 211–222
 Lanctot K, Li M, Ma B, Wang S, Zhang L (1999) Distinguishing string selection problems. In: Proc. 6th Ann. ACMSIAM Symp. on Discrete Algorithms, pp 633–642
 Li M, Ma B, Wang L (1999) Finding similar regions in many strings. In: Proc. 31st ACM Symp. on Theory of Computing (STOC’99), pp 473–482
 Maier D (1978) The complexity of some problems on subsequences and supersequences. J ACM 25:322–336 CrossRef
 Nussinov R, Pieczenik G, Griggs J, Kleitman D (1978) Algorithms for loop matching. SIAM J Appl Math 35:68–82 CrossRef
 Rick C (2000) Efficient computation of all longest common subsequences. In: Proc. 7th Scandinavian Workshop on Algorithm Theory (SWAT’00), pp 407–418
 Rivas E, Eddy SR (1999) A dynamic programming algorithm for RNA structure prediction including pseudoknots. J Mol Biol 285:2053–2068 CrossRef
 Smith TF, Waterman MS (1981) Identification of common molecular subsequences. J Mol Biol 147:195–197 CrossRef
 Tsai YT (2003) The constrained longest common subsequence problem. Inform Proc Lett 88(4):173–176
 Zucker M, Stiegler P (1981) Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res 9:133–148
 Zucker M (1989) Computer prediction of RNA structure. Methods Enzymol 180:262–288 CrossRef
 Title
 RNA multiple structural alignment with longest common subsequences
 Journal

Journal of Combinatorial Optimization
Volume 13, Issue 2 , pp 179188
 Cover Date
 20070201
 DOI
 10.1007/s108780069020x
 Print ISSN
 13826905
 Online ISSN
 15732886
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 RNA multiple structure alignment
 Longest common subsequence
 Dynamic programming
 Industry Sectors
 Authors

 Sergey Bereg ^{(1)}
 Marcin Kubica ^{(2)}
 Tomasz Waleń ^{(2)}
 Binhai Zhu ^{(3)}
 Author Affiliations

 1. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 750830688, USA
 2. Institute of Informatics, Warsaw University, Banacha 2, 02097, Warszawa, Poland
 3. Department of Computer Science, Montana State University, Bozeman, MT, 597173880, USA