Computing the similarity of two sequences with nested arc annotations

  • Authors:

  • Jochen Alber;Jens Gramm;Jiong Guo;Rolf Niedermeier

  • Affiliations:

  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Federal Republic of Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Federal Republic of Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Federal Republic of Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Federal Republic of Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

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Abstract

We present exact algorithms for the NP-complete LONGEST COMMON SUBSEQUENCE problem for sequences with nested arc annotations, a problem occurring in structure comparison of RNA. Given two sequences of length at most n and nested arc structure, one of our algorithms determines (if existent) in O(3.31k1+k2 ċ n) time an arc-preserving subsequence of both sequences, which can be obtained by deleting (together with corresponding arcs) k1 letters from the first and k2 letters from the second sequence. A second algorithm shows that, (in case of a four letter alphabet) we can find a length l arc-annotated subsequence in O(12lċlċn) time. This means that the problem is fixed-parameter tractable when parameterized by the number of deletions as well as when parameterized by the subsequence length. Our findings complement known approximation results which give a quadratic time factor-2-approximation for the general and polynomial time approximation schemes for restricted versions of the problem. In addition, we obtain further fixed-parameter tractability results for these restricted versions.