Low distortion embeddings for edit distance
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The intractability of computing the Hamming distance
Theoretical Computer Science
Nonembeddability theorems via Fourier analysis
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Oblivious string embeddings and edit distance approximations
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A dictionary for approximate string search and longest prefix search
CIKM '06 Proceedings of the 15th ACM international conference on Information and knowledge management
A relation between edit distance for ordered trees and edit distance for Euler strings
Information Processing Letters
An Efficient Web Page Change Detection System Based on an Optimized Hungarian Algorithm
IEEE Transactions on Knowledge and Data Engineering
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Low distortion embeddings for edit distance
Journal of the ACM (JACM)
Edit distance for a run-length-encoded string and an uncompressed string
Information Processing Letters
Vector representations for efficient comparison and search for similar strings
Cybernetics and Systems Analysis
An approach for continuous inspection of source code
Proceedings of the 6th international workshop on Software quality
Sketching in adversarial environments
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Self-tuning query mesh for adaptive multi-route query processing
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
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
Foundations and Trends in Databases
Space lower bounds for online pattern matching
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Locally consistent parsing and applications to approximate string comparisons
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
The smoothed complexity of edit distance
ACM Transactions on Algorithms (TALG)
Improved sketching of hamming distance with error correcting
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Efficient communication protocols for deciding edit distance
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Space lower bounds for online pattern matching
Theoretical Computer Science
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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Edit distance has been extensively studied for the past several years. Nevertheless, no linear-time algorithm is known to compute the edit distance between two strings, or even to approximate it to within a modest factor. Furthermore, for various natural algorithmic problems such as low-distortion embeddings into normed spaces, approximate nearest-neighbor schemes, and sketching algorithms, known results for the edit distance are rather weak. We develop algorithms that solve gap versions of the edit distance problem: given two strings of length n with the promise that their edit distance is either at most k or greater than \ell, decide which of the two holds. We present two sketching algorithms for gap versions of edit distance. Our first algorithm solves the k vs.(kn)^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} gap problem, using a constant size sketch. A more involved algorithm solves the stronger k vs. \ell gap problem, where \ell can be as small as O(k虏) 驴 still with a constant sketch 驴 but works only for strings that are mildly "non-repetitive". Finally, we develop an n^{{3 \mathord{\left/ {\vphantom {3 7}} \right. \kern-\nulldelimiterspace} 7}}-approximation quasi-linear time algorithm for edit distance, improving the previous best factor of n^{{3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-\nulldelimiterspace} 4}} [5]; if the input strings are assumed to be non-repetitive, then the approximation factor can be strengthened to n^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}.