Probabilistic counting algorithms for data base applications
Journal of Computer and System Sciences
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
ACM Computing Surveys (CSUR)
Approximate counting of inversions in a data stream
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Similarity estimation techniques from rounding algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximate nearest neighbor algorithms for Frechet distance via product metrics
Proceedings of the eighteenth annual symposium on Computational geometry
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On approximate nearest neighbors under I norm
Journal of Computer and System Sciences
Lectures on Discrete Geometry
A sublinear algorithm for weakly approximating edit distance
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximate Nearest Neighbor under edit distance via product metrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Euclidean distortion and the sparsest cut
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Space efficient mining of multigraph streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An improved data stream summary: the count-min sketch and its applications
Journal of Algorithms
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Nonembeddability theorems via Fourier analysis
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Efficient algorithms for substring near neighbor problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Planar Earthmover is not in L_1
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A near linear time constant factor approximation for Euclidean bichromatic matching (cost)
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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)
Estimating the distance to a monotone function
Random Structures & Algorithms
The Computational Hardness of Estimating Edit Distance [Extended Abstract]
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Earth mover distance over high-dimensional spaces
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The Smoothed Complexity of Edit Distance
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Information complexity: a tutorial
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Near-optimal sublinear time algorithms for Ulam distance
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for edit distance and product metrics via Poincaré-type inequalities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Computational Hardness of Estimating Edit Distance
SIAM Journal on Computing
Streaming algorithms with one-sided estimation
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
The smoothed complexity of edit distance
ACM Transactions on Algorithms (TALG)
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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A common approach for solving computational problems over a difficult metric space is to embed the "hard" metric into L1 which admits efficient algorithms and is thus considered an "easy" metric. This approach has proved successful or partially successful for important spaces such as the edit distance, but it also has inherent limitations: it is provably impossible to go below certain approximation for some metrics. We propose a new approach, of embedding the difficult space into richer host spaces, namely iterated products of standard spaces like l1 and l∞. We show that this class is rich since it contains useful metric spaces with only a constant distortion, and, at the same time, it is tractable and admits efficient algorithms. Using this approach, we obtain for example the first nearest neighbor data structure with O(log log d) approximation for edit distance in non-repetitive strings (the Ulam metric). This approximation is exponentially better than the lower bound for embedding into L1. Furthermore, we give constant factor approximation for two other computational problems. Along the way, we answer positively a question posed in [Ajtai, Jayram, Kumar, and Sivakumar, STOC 2002]. One of our algorithms has already found applications for smoothed edit distance over 0--1 strings [Andoni and Krauthgamer, ICALP 2008].