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Towards Optimally Solving the LongestCommonSubsequenceProblem for Sequences with Nested Arc Annotations in Linear Time

  • Jochen Alber
  • Jens Gramm
  • Jiong Guo
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2373)

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, our algorithm determines (if existent) in time \( O(3.31^{k_1 + k_2 } \cdot n) \) an arc-preserving subsequence of both sequences, which can be obtained by deleting (together with corresponding arcs) k 1 letters from the first and k 2 letters from the second sequence. Thus, the problem is fixed-parameter tractable when parameterized by the number of deletions. This complements 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.

Keywords

Search Tree Input Sequence Exact Algorithm Recursive Call Restricted Version 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jochen Alber
    • 1
  • Jens Gramm
    • 1
  • Jiong Guo
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenFed. Rep. of Germany

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