Speeding up dynamic programming with application to molecular biology
Theoretical Computer Science
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
Sparse dynamic programming I: linear cost functions
Journal of the ACM (JACM)
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
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
String editing and longest common subsequences
Handbook of formal languages, vol. 2
Dynamic programming: special cases
Pattern matching algorithms
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
A task-based architecture for application-aware adjuncts
Proceedings of the 5th international conference on Intelligent user interfaces
On the shared substring alignment problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A fast algorithm for computing longest common subsequences
Communications of the ACM
On the common substring alignment problem
Journal of Algorithms
A sub-quadratic sequence alignment algorithm for unrestricted cost matrices
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Visualization and Analysis of Clickstream Data of Online Stores for Understanding Web Merchandising
Data Mining and Knowledge Discovery
Data mining for path traversal patterns in a web environment
ICDCS '96 Proceedings of the 16th International Conference on Distributed Computing Systems (ICDCS '96)
Dynamic programming algorithms for the mosaic longest common subsequence problem
Information Processing Letters
Efficient algorithms for finding interleaving relationship between sequences
Information Processing Letters
LCS Approximation via Embedding into Local Non-repetitive Strings
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
LCS approximation via embedding into locally non-repetitive strings
Information and Computation
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The "Common Substring Alignment" problem is defined as follows. The input consists of a set of strings S1, S2...,Sc, with a common substring appearing at least once in each of them, and a target string T. The goal is to compute similarity of all strings Si with T, without computing the part of the common substring over and over again.In this paper we consider the Common Substring Alignment problem for the LCS (Longest Common Subsequence) similarity metric. Our algorithm gains its efficiency by exploiting the sparsity inherent to the LCS problem. Let Y be the common substring, n be the size of the compared sequences, Ly be the length of the LCS of T and Y, denoted |LCS[T, Y]|, and L be max{|LCS[T, Si]|}. Our algorithm consists of an O(nLy) time encoding stage that is executed once per common substring, and an O(L) time alignment stage that is executed once for each appearance of the common substring in each source string. The additional running time depends only on the length of the parts of the strings that are not in any common substring.