Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
A Space-Economical Suffix Tree Construction Algorithm
Journal of the ACM (JACM)
Lower bounds for embedding edit distance into normed spaces
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A sublinear algorithm for weakly approximating edit distance
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Efficient approximate and dynamic matching of patterns using a labeling paradigm
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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
Nonembeddability theorems via Fourier analysis
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximating edit distance in near-linear time
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
The Computational Hardness of Estimating Edit Distance
SIAM Journal on Computing
Approximating tree edit distance through string edit distance
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The smoothed complexity of edit distance
ACM Transactions on Algorithms (TALG)
Homomorphic fingerprints under misalignments: sketching edit and shift distances
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We introduce an oblivious embedding that maps strings of length n under edit distance to strings of length at most n/r under edit distance for any value of parameter r. For any given r, our embedding provides a distortion of Õ(r1+μ) for some μ = o(1), which we prove to be (almost) optimal. The embedding can be computed in Õ(21/μn) time.We also show how to use the main ideas behind the construction of our embedding to obtain an efficient algorithm for approximating the edit distance between two strings. More specifically, for any 1 ε ≥ 0, we describe an algorithm to compute the edit distance D(S, R) between two strings S and R of length n in time Õ(n1+ε), within an approximation factor of min{n1-ε/3+o(1), (D(S, R/nε)1/2+o(1)}. For the case of ε = 0, we get a Õ(n)-time algorithm that approximates the edit distance within a factor of min{n1/3+o(1), D(S, R)1/2+o(1)}, improving the recent result of Bar-Yossef et al. [2].