On the computational complexity of 2-interval pattern matching problems,☆☆

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Abstract

The focus of this paper is on the computational complexity of pattern matching problems over set of 2-intervals. These problems occur in the context of molecular biology when a structured pattern, i.e., a RNA secondary structure given in the form of a 2-interval pattern, has to be found in a sequence database. We show that finding a 2-interval pattern in a set of 2-intervals is a NP-complete problem even if no 2-interval of the pattern precedes the other, but can be solved in polynomial time for several interesting special cases. In particular, it is shown that the pseudo-knot free RNA secondary structure case is polynomial time solvable in our 2-interval formalism. Also, we investigate the computational complexity of finding the longest 2-interval pattern in a set of 2-intervals and prove several NP-completeness results as well as polynomial time solvable special cases.

Keywords

RNA secondary structure
2-Interval
Pattern matching
NP-completeness

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A preliminary version of the paper appears in Proceedings of the CPM 2002, Springer LNCS, Vol. 2373, pp. 53–63, Fukuoka, Japan, July, 2002.

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The work described in this paper was developed in part during the author's Ph.D. at LIAFA laboratory, Université Paris 7, 2, place Jussieu F-75251 Paris Cedex 05, France.