Speeding up dynamic programming with application to molecular biology
Theoretical Computer Science
Text compression
A linear-time algorithm for concave one-dimensional dynamic programming
Information Processing Letters
Sequence comparison with mixed convex and concave costs
Journal of Algorithms
An almost linear time algorithm for generalized matrix searching
SIAM Journal on Discrete Mathematics
Efficient parallel algorithms for string editing and related problems
SIAM Journal on Computing
Sparse dynamic programming II: convex and concave cost functions
Journal of the ACM (JACM)
Text algorithms
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
A space efficient algorithm for finding the best nonoverlapping alignment score
Theoretical Computer Science
An Algorithm for Locating Nonoverlapping Regions of Maximum Alignment Score
SIAM Journal on Computing
Let sleeping files lie: pattern matching in Z-compressed files
Journal of Computer and System Sciences
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Dynamic programming: special cases
Pattern matching algorithms
SIAM Journal on Computing
On the shared substring alignment problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the common substring alignment problem
Journal of Algorithms
A Text Compression Scheme That Allows Fast Searching Directly in the Compressed File
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Almost Optimal Fully LZW-Compressed Pattern Matching
DCC '99 Proceedings of the Conference on Data Compression
Faster Approximate String Matching over Compressed Text
DCC '01 Proceedings of the Data Compression Conference
Edit distance of run-length encoded strings
Information Processing Letters
Algorithms for Transposition Invariant String Matching
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Sparse LCS common substring alignment
Information Processing Letters
Information Processing Letters
Transposition invariant string matching
Journal of Algorithms
Faster Algorithms for Optimal Multiple Sequence Alignment Based on Pairwise Comparisons
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Comparing Compressed Sequences for Faster Nucleotide BLAST Searches
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
New efficient algorithms for the LCS and constrained LCS problems
Information Processing Letters
Algorithms for computing variants of the longest common subsequence problem
Theoretical Computer Science
A New Efficient Algorithm for Computing the Longest Common Subsequence
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Alignment of biological sequences with quality scores
International Journal of Bioinformatics Research and Applications
Privacy-preserving genomic computation through program specialization
Proceedings of the 16th ACM conference on Computer and communications security
Transposition invariant string matching
Journal of Algorithms
An improved algorithm for generalized comparison of minisatellites
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Sparse LCS common substring alignment
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Protein similarity search with subset seeds on a dedicated reconfigurable hardware
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Pattern matching in pseudo real-time
Journal of Discrete Algorithms
Rapid homology search with two-stage extension and daughter seeds
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Faster algorithms for optimal multiple sequence alignment based on pairwise comparisons
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Fully incremental LCS computation
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
A comparison of index-based lempel-Ziv LZ77 factorization algorithms
ACM Computing Surveys (CSUR)
Speeding up HMM decoding and training by exploiting sequence repetitions
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Algorithms for computing the longest parameterized common subsequence
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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The classical algorithm for computing the similarity between two sequences [36, 39] uses a dynamic programming matrix, and compares two strings of size n in O(n2) time. We address the challenge of computing the similarity of two strings in sub-quadratic time, for metrics which use a scoring matrix of unrestricted weights. Our algorithm applies to both local and global alignment computations.The speed-up is achieved by dividing the dynamic programming matrix into variable sized blocks, as induced by Lempel-Ziv parsing of both strings, and utilizing the inherent periodic nature of both strings. This leads to an O(n2/log n) algorithm for an input of constant alphabet size. For most texts, the time complexity is actually O(hn2/log n) where h ≤ 1 is the entropy of the text.