The 2-Interval Pattern problem over its various models and restrictions was proposed by Vialette for RNA secondary structure prediction, and has attracted a lot of attention from the theoretical computer science community in recent years. In the framework of 2-intervals, the preceding-and-crossing model is an especially interesting model for RNA secondary structures with pseudoknots. In this paper, we present a polynomial time approximation scheme for the Weighted 2-Interval Pattern problem over the preceding-and-crossing model. Our algorithm improves the previous best 2-approximation algorithm, and closes this problem in terms of the approximation ratio.
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