Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A Faster Algorithm for RNA Co-folding
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
A worst-case and practical speedup for the RNA co-folding problem using the four-Russians idea
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Sparsification of RNA structure prediction including pseudoknots
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Reducing the worst case running times of a family of RNA and CFG problems, using Valiant's approach
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Sparse RNA folding: Time and space efficient algorithms
Journal of Discrete Algorithms
Rich parameterization improves RNA structure prediction
RECOMB'11 Proceedings of the 15th Annual international conference on Research in computational molecular biology
Time and space efficient RNA-RNA interaction prediction via sparse folding
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
Exact pattern matching for RNA structure ensembles
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
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The classical algorithm for RNA single strand folding requires O (n Z ) time and O (n 2) space, where n denotes the length of the input sequence and Z is a sparsity parameter that satisfies n ≤ Z ≤ n 2. We show how to reduce the space complexity of this algorithm. The space reduction is based on the observation that some solutions for subproblems are not examined after a certain stage of the algorithm, and may be discarded from memory. This yields an O (nZ ) time and O (Z ) space algorithm, that outputs both the cardinality of the optimal folding as well as a corresponding secondary structure. The space-efficient approach also extends to the related RNA simultaneous alignment with folding problem, and can be applied to reduce the space complexity of the fastest algorithm for this problem from O (n 2 m 2) down to $O(nm^2 + \tilde{Z})$, where n and m denote the lengths of the input sequences to be aligned, and $\tilde{Z}$ is a sparsity parameter that satisfies n m ≤ $\tilde{Z}$ ≤ n 2 m 2. In addition, we also show how to speed up the base-pairing maximization variant of RNA single strand folding. The speed up is achieved by combining two independent existing techniques, which restrict the number of expressions that need to be examined in bottleneck computations of these algorithms. This yields an O (LZ ) time and O (Z ) space algorithm, where L denotes the maximum cardinality of a folding of the input sequence. Additional online supporting material may be found at: http://www.cs.bgu.ac.il/zakovs/RNAfold/CPM09_supporting_material.pdf