Abstract
We study the computational complexity of pattern matching problems over 2-interval sets. These problems occur in the context of molecular biology when a structured pattern, i.e., a RNA secondary structure, has to be found in a sequence. We show that the Pattern Matching Over 2-Interval Set problem is NP-complete for structured patterns where no pair precedes the other, but can be solved in polynomial time for several interesting special cases.
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References
B. Billoud, M. Kontic, and A. Viari. Palingol: a declarative programming language to describe nucleic acids secondary structures and to scan sequence database. Nucl. Acids Res., 24:1395–403, 1996.
I. Dagan, M. C. Golumbic, and R. Y. Pinter. Trapezoid graphs and their coloring. Discrete Appl. Math., 21:35–46, 1988.
P. Evans. Finding common subsequences with arcs and pseudoknots. In Proceedings of the 10th Annual Symposium Combinatorial Pattern Matching (CPM 1999), volume 1645 of Lecture Notes in Computer Science, pages 270–280, 1999.
S. Felsner, R. Müller, and L. Wernisch. Trapezoid graphs and generalizations: Geometry and algorithms. Discrete Appl. Math., 74:13–32, 1997.
M. R. Garey and D. S. Johnson. Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman, San Franciso, 1979.
F. Gavril. Algorithms for a maximum clique and a minimum independent set of a circle graph. Networks, 3:261–273, 1973.
D. Goldman, S. Istrail, and C. H. Papadimitriou. Algorithmic aspects of protein structure similarity. In IEEE Proceedings of the 40th Annual Conference of Foundations of Computer Science (FOCS99), pages 512–521, 1999.
M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
U. I. Gupta, D. T. Lee, and J.Y-T. Leung. Efficient algorithms for interval graph and circular-arc graphs. Networks, 12:459–467, 1982.
T. Jiang, G.-H. Lin, B. Ma, and K. Zhang. The longest common subsequence problem for arc-annotated sequences. In Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching (CPM 2000), volume 1848 of Lecture Notes in Computer Science, pages 154–165, 2000.
P. Kilpeläinen. Tree matching problems with applications to structured text databases. PhD thesis, University of Helsinki, Finland, 1992.
E. L. Lawler and D. W. Wood. Branch and bound methods: A survey. Operations Research, 14:699–719, 1966.
S. Vialette. Aspects algorithmiques de la pr’ediction des structures secondaires d’ARN. PhD thesis, Universit’e Denis Diderot, Paris, France, 2001. (in french).
D. B. West and D. B. Shmoys. Recognizing graphs with fixed interval number is NP-complete. Discrete Appl. Math., 8:295–305, 1984.
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Vialette, S. (2002). Pattern Matching Problems over 2-Interval Sets. In: Apostolico, A., Takeda, M. (eds) Combinatorial Pattern Matching. CPM 2002. Lecture Notes in Computer Science, vol 2373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45452-7_6
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DOI: https://doi.org/10.1007/3-540-45452-7_6
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