Extracting constrained 2-interval subsets in 2-interval sets
نویسندگان
چکیده
2-interval sets were used in [28,29] for establishing a general representation for macroscopic describers of RNA secondary structures. In this context, we have a 2-interval for each legal local fold in a given RNA sequence, and a constrained pattern made of disjoint 2-intervals represents a putative RNA secondary structure. We focus here on the problem of extracting a constrained pattern in a set of 2intervals. More precisely, given a set of 2-intervals D and a model R describing if two disjoint 2-intervals in a solution can be in precedence order (<), be allowed to nest ( ) and/or be allowed to cross ( ), we consider the problem of finding a maximum cardinality subset D′ ⊆ D of disjoint 2-intervals such that any two 2intervals in D′ agree with R. The different combinations of restrictions on model R alter the computational complexity of the problem, and need to be examined separately. In this paper, we improve the time complexity of [29] for model R = { } by giving an optimal O(n log n) time algorithm, where n is the cardinality of the 2-interval set D. We also give a graph-like relaxation for model R = { , } that is solvable in O(n2 √ n) time. Finally, we prove that the considered problem is NP-complete for model R = {<, } even for same-length intervals, and give a fixed-parameter tractability result based on the crossing structure of D.
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ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 385 شماره
صفحات -
تاریخ انتشار 2007