Polynomial algorithms for protein similarity search for restricted mRNA structures

  • Authors:

  • Frank Gurski

  • Affiliations:

  • Heinrich-Heine-Universität Düsseldorf, Institute of Computer Science, D-40225 Düsseldorf, Germany

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

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Abstract

In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [R. Backofen, N.S. Narayanaswamy, F. Swidan, On the complexity of protein similarity search under mRNA structure constraints, in: Proceedings of the Annual Symposium of Theoretical Aspects of Computer Science, in: LNCS, vol. 2285, Springer, 2002, pp. 274-286] denoted as the MRSO problem. The problem is known to be NP-complete for planar associated implied structure graphs of vertex degree at most 3. In [G. Blin, G. Fertin, D. Hermelin, S. Vialette, Fixed-parameter algorithms for protein similarity search under mRNA structure constraints, in: Proceedings of Graph-Theoretical Concepts in Computer Science, in: LNCS, vol. 3787, Springer, 2005, pp. 271-282] a first polynomial dynamic programming algorithms for MRSO on implied structure graphs with maximum vertex degree 3 of bounded cut-width is shown. We give a simple but much more general polynomial dynamic programming solution for the MRSO problem for associated implied structure graphs of bounded clique-width. Our result implies that MRSO is polynomial for graphs of bounded tree-width, co-graphs, P"4-sparse graphs, and distance hereditary graphs. Further we conclude that the problem of comparing two solutions for MRSO is hard for the class P"@?^N^P, which is defined as the set of problems which can be solved in polynomial time with a number of parallel queries to an oracle in NP.