Efficient algorithms for regular expression constrained sequence alignment

Imposing constraints in the form of a finite automaton or a regular expression is an effective way to incorporate additional a priori knowledge into sequence alignment procedures. With this motivation, the Regular Expression Constrained Sequence Alignment Problem was introduced, which proposed an O(n 2 t 4 ) time and O(n 2 t 2 ) space algorithm for solving it, where n is the length of the input strings and t is the number of states in the input non-deterministic automaton. A faster O(n 2 t 3 ) time algorithm for the same problem was subsequently proposed. In this article, we further speed up the algorithms for Regular Language Constrained Sequence Alignment by reducing their worst case time complexity bound to O(n 2 t 3 /log t). This is done by establishing an optimal bound on the size of Straight-Line Programs solving the maxima computation subproblem of the basic dynamic programming algorithm. We also study another solution based on a Steiner Tree computation. While it does not improve the worst case, our simulations show that both approaches are efficient in practice, especially when the input automata are dense.

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Constrained sequence alignment: A general model and the hardness results

Chung

Tang

2007

Discrete Applied Mathematics

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Imposing constraints is a way to incorporate information into the sequence alignment procedure. In this paper, a general model for constrained alignment is proposed so that analyses admitted are more flexible and that different pattern definitions can be treated in a simple unified way. We give a polynomial time algorithm for pairwise constrained alignment for the generalized formulation, and prove the inapproximability of the problem when the number of sequences can be arbitrary. In addition, previous works deal only with the case that the patterns in the constraint have to occur in the output alignment in the same order as that specified by the input. It is of both theoretical and practical interest to investigate the case when the order is no longer limited. We show that the problem is not approximable even when the number of sequences is two. We also give the NPO-completeness results for the problems with bounds imposed on the objective function value.

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Efficient algorithms for regular expression constrained sequence alignment

Cited by 8 publications

References 13 publications

A Linear-Space Algorithm for the Substring Constrained Alignment Problem

A Linear-Space Algorithm for the Substring Constrained Alignment Problem

Regular Language Constrained Sequence Alignment Revisited

Constrained sequence alignment: A general model and the hardness results

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