Fast string matching with k-differences
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
The String-to-String Correction Problem
Journal of the ACM (JACM)
Bounds on the Complexity of the Longest Common Subsequence Problem
Journal of the ACM (JACM)
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
A fast algorithm for computing longest common subsequences
Communications of the ACM
On the common substring alignment problem
Journal of Algorithms
Longest Common Subsequence from Fragments via Sparse Dynamic Programming
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Rapid identification of repeated patterns in strings, trees and arrays
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
A Subquadratic Sequence Alignment Algorithm for Unrestricted Scoring Matrices
SIAM Journal on Computing
Sparse LCS common substring alignment
Information Processing Letters
Efficient randomized pattern-matching algorithms
IBM Journal of Research and Development - Mathematics and computing
Approximating Edit Distance Efficiently
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Low distortion embeddings for edit distance
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Oblivious string embeddings and edit distance approximations
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The Computational Hardness of Estimating Edit Distance [Extended Abstract]
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Approximate String Matching with Address Bit Errors
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Computing a longest increasing subsequence of length k in time O(n log log k)
VoCS'08 Proceedings of the 2008 international conference on Visions of Computer Science: BCS International Academic Conference
| Hi-index | 0.00 |
A classical measure of similarity between strings is the length of the longest common subsequence (LCS) between the two given strings. The search for efficient algorithms for finding the LCS has been going on for more than three decades. To date, all known algorithms may take quadratic time (shaved by logarithmic factors) to find large LCS. In this paper the problem of approximating LCS is studied, while focusing on the hard inputs for this problem, namely, approximating LCS of near-linear size in strings over relatively large alphabet (of size at least n *** for some constant *** 0, where n is the length of the string). We show that, any given string over relatively large alphabet can be embedded into a local non-repetitive string. This embedding has a negligible additive distortion for strings that are not too dissimilar in terms of the edit distance. We also show that LCS can be efficiently approximated in locally-non-repetitive strings.