Approximation of RNA multiple structural alignment

  • Authors:

  • Marcin Kubica;Romeo Rizzi;Stéphane Vialette;Tomasz Waleń

  • Affiliations:

  • Institute of Informatics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland;Dipartimento di Matematica ed Informatica (DIMI), Universití di Udine, Via delle Scienze 208, I-33100 Udine, Italy;LIGM, CNRS UMR 8049, Université Paris-Est Marne-la-Vallée, 5 Bd Descartes, 77454 Marne-la-Vallée, France;Institute of Informatics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2011

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Abstract

In the context of non-coding RNA (ncRNA) multiple structural alignment, Davydov and Batzoglou (2006) introduced in [7] the problem of finding the largest nested linear graph that occurs in a set G of linear graphs, the so-called Max-NLS problem. This problem generalizes both the longest common subsequence problem and the maximum common homeomorphic subtree problem for rooted ordered trees. In the present paper, we give a fast algorithm for finding the largest nested linear subgraph of a linear graph and a polynomial-time algorithm for a fixed number (k) of linear graphs. Also, we strongly strengthen the result of Davydov and Batzoglou (2006) [7] by proving that the problem is NP-complete even if G is composed of nested linear graphs of height at most 2, thereby precisely defining the borderline between tractable and intractable instances of the problem. Of particular importance, we improve the result of Davydov and Batzoglou (2006) [7] by showing that the Max-NLS problem is approximable within ratio O(logm"o"p"t) in O(kn^2) running time, where m"o"p"t is the size of an optimal solution. We also present O(1)-approximation of Max-NLS problem running in O(kn) time for restricted linear graphs. In particular, for ncRNA derived linear graphs, a 14-approximation is presented.