Algorithms for the Constrained Longest Common Subsequence Problems

Arslan, Abdullah N.; Eğecioǧlu, Ömer

doi:10.1142/s0129054105003674

“…This is achieved based on recent algorithms which take as input a regular expression of length r and convert it into an e-free NFA with O(r) states and O(r log 2 r) transitions (Hromkoviěc et al, 2001;Schnitger, 2006;Geffert, 2003). This yields an O(n 2 r 2 log 2 r) time and O(n 2 r 2 ) space complexities for the algorithm of Chung et al We note that this was not observed by Arslan and Egecioglu (2005) and Chung et al (2007b).…”

Section: Resultsmentioning

confidence: 83%

“…Various extensions of the Smith-Waterman algorithm (Smith and Waterman, 1981) modify the alignment considerations according to a priori knowledge (Arslan and Egecioglu, 2005;Chen and Chao, 2009;Iliopoulos and Rahman, 2008;Peng and Ting, 2005;Tsai, 2003;Sunyaev et al, 2004;Gotthilf et al, 2008). One kind of a priori knowledge is about shared properties (patterns), which are expected to be preserved by the alignment.…”

Section: Introduction Smentioning

confidence: 99%

Regular Language Constrained Sequence Alignment Revisited

Kucherov

¹

,

Pinhas

²

,

Ziv-Ukelson

³

2011

Journal of Computational Biology

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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, 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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“…Various extensions of the Smith-Waterman algorithm (Smith and Waterman, 1981) modify the alignment considerations according to a priori knowledge (Arslan and Egecioglu, 2005;Chen and Chao, 2009;Iliopoulos and Rahman, 2008;Peng and Ting, 2005;Tsai, 2003;Sunyaev et al, 2004;Gotthilf et al, 2008). One kind of a priori knowledge is about shared properties (patterns), which are expected to be preserved by the alignment.…”

Section: Introduction Smentioning

confidence: 99%

Regular Language Constrained Sequence Alignment Revisited

Kucherov

¹

,

Pinhas

²

,

Ziv-Ukelson

³

2011

Lecture Notes in Computer Science

0

View full text Add to dashboard Cite

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.

show abstract

“…Later, Chin et al [6] and independently, Arslan and Egecioglu [2,3] presented improved algorithms with O(pn 2 ) time and space complexity.…”

Section: Introductionmentioning

confidence: 99%