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Fast RNA structure alignment for crossing input structures. (English) Zbl 1247.68105
Kucherov, Gregory (ed.) et al., Combinatorial pattern matching. 20th annual symposium, CPM 2009, Lille, France, June 22–24, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-02440-5/pbk). Lecture Notes in Computer Science 5577, 236-248 (2009).
Summary: The complexity of pairwise RNA structure alignment depends on the structural restrictions assumed for both the input structures and the computed consensus structure. For arbitrarily crossing input and consensus structures, the problem is NP-hard. For non-crossing consensus structures, T. Jiang et al.’s algorithm [“A general edit distance between RNA structures”, J. Comput. Biology 9, No. 2, 371–388 (2002)] computes the alignment in \(O(n ^{2} m ^{2})\) time where \(n\) and \(m\) denote the lengths of the two input sequences. If also the input structures are non-crossing, the problem corresponds to tree editing which can be solved in \(O(m^2n(1+\log\frac{n}{m}))\) time. We present a new algorithm that solves the problem for \(d\)-crossing structures in \(O(d m ^{2} n \log n)\) time, where \(d\) is a parameter that is one for non-crossing structures, bounded by \(n\) for crossing structures, and much smaller than \(n\) on most practical examples. Crossing input structures allow for applications where the input is not a fixed structure but is given as base-pair probability matrices.
For the entire collection see [Zbl 1165.68013].

68Q25 Analysis of algorithms and problem complexity
68W32 Algorithms on strings
92D20 Protein sequences, DNA sequences
Full Text: DOI
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