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.
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.