The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Multicast algorithms for hypercube multiprocessors
Journal of Parallel and Distributed Computing
Translating regular expressions into small εe-free nondeterministic finite automata
Journal of Computer and System Sciences
Multicast Communication in Multicomputer Networks
IEEE Transactions on Parallel and Distributed Systems
Journal of Computer and System Sciences
The constrained longest common subsequence problem
Information Processing Letters
The Rectilinear Steiner Arborescence Problem Is NP-Complete
SIAM Journal on Computing
Efficient algorithms for regular expression constrained sequence alignment
Information Processing Letters
Regular expression constrained sequence alignment
Journal of Discrete Algorithms
New efficient algorithms for the LCS and constrained LCS problems
Information Processing Letters
On the generalized constrained longest common subsequence problems
Journal of Combinatorial Optimization
Regular expressions and NFAs without Ε-transitions
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Time and space efficient algorithms for constrained sequence alignment
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
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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, Arslan [1] introduced the Regular Language Constrained Sequence Alignment Problem and proposed an O(n2t4) time and O(n2t2 space algorithm for solving it, where n is the length of the input strings and t is the number of states in the non-deterministic automaton, which is given as input. Chung et al. [2] proposed a faster O(n2t3) time algorithm for the same problem. In this paper, we further speed up the algorithms for Regular Language Constrained Sequence Alignment by reducing their worst case time complexity bound to O(n2t3/ 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 run time complexity in the worst case, our simulations show that both approaches are efficient in practice, especially when the input automata are dense.