How to Compare Arc-Annotated Sequences: The Alignment Hierarchy

We describe a new unifying framework to express comparison of arc-annotated sequences, which we call alignment of arc-annotated sequences. We first prove that this framework encompasses main existing models, which allows us to deduce complexity results for several cases from the literature. We also show that this framework gives rise to new relevant problems that have not been studied yet. We provide a thorough analysis of these novel cases by proposing two polynomial time algorithms and an NP-completeness proof. This leads to an almost exhaustive study of alignment of arc-annotated sequences.

[1]  Gad M. Landau,et al.  Approximating the 2-interval pattern problem , 2005, Theor. Comput. Sci..

[2]  Stefano Leonardi,et al.  Algorithms - ESA 2005, 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005, Proceedings , 2005, ESA.

[3]  Zhi-Zhong Chen,et al.  The longest common subsequence problem for sequences with nested arc annotations , 2002, J. Comput. Syst. Sci..

[4]  Stéphane Vialette,et al.  On the computational complexity of 2-interval pattern matching problems , 2004, Theor. Comput. Sci..

[5]  Bin Ma,et al.  Computing similarity between RNA structures , 1999, Theor. Comput. Sci..

[6]  Tao Jiang,et al.  Alignment of Trees - An Alternative to Tree Edit , 1994, Theor. Comput. Sci..

[7]  Goos Kant,et al.  On Triangulating Planar Graphs under the Four-Connectivity Constraint , 1994, Algorithmica.

[8]  Philip N. Klein,et al.  Computing the Edit-Distance between Unrooted Ordered Trees , 1998, ESA.

[9]  Bin Ma,et al.  The Longest Common Subsequence Problem for Arc-Annotated Sequences , 2000, CPM.

[10]  Kaizhong Zhang,et al.  Simple Fast Algorithms for the Editing Distance Between Trees and Related Problems , 1989, SIAM J. Comput..

[11]  Paul C. Kainen,et al.  The book thickness of a graph , 1979, J. Comb. Theory, Ser. B.

[12]  Kuo-Chung Tai,et al.  The Tree-to-Tree Correction Problem , 1979, JACM.

[13]  Bin Ma,et al.  The longest common subsequence problem for arc-annotated sequences , 2004, J. Discrete Algorithms.

[14]  Michael R. Fellows,et al.  Algorithms and complexity for annotated sequence analysis , 1999 .

[15]  Bin Ma,et al.  Edit distance between two RNA structures , 2001, RECOMB.

[16]  Guillaume Fertin,et al.  RNA sequences and the EDIT ( NESTED , NESTED ) problem , 2003 .

[17]  Bin Ma,et al.  A General Edit Distance between RNA Structures , 2002, J. Comput. Biol..

[18]  Hélène Touzet,et al.  Decomposition algorithms for the tree edit distance problem , 2005, J. Discrete Algorithms.