The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
Lectures on Discrete Geometry
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
SIAM Journal on Computing
Lower bounds for embedding edit distance into normed spaces
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity
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
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Low distortion embeddings for edit distance
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved lower bounds for embeddings into L1
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
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating edit distance in near-linear time
Proceedings of the forty-first annual ACM symposium on Theory of computing
Hellinger Strikes Back: A Note on the Multi-party Information Complexity of AND
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
The Data Stream Space Complexity of Cascaded Norms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Information complexity: a tutorial
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The Computational Hardness of Estimating Edit Distance
SIAM Journal on Computing
The streaming complexity of cycle counting, sorting by reversals, and other problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The smoothed complexity of edit distance
ACM Transactions on Algorithms (TALG)
| Hi-index | 0.00 |
We prove that any sketching protocol for edit distance achieving a constant approximation requires nearly logarithmic (in the strings' length) communication complexity. This is an exponential improvement over the previous, doubly-logarithmic, lower bound of [Andoni-Krauthgamer, FOCS'07]. Our lower bound also applies to the Ulam distance (edit distance over non-repetitive strings). In this special case, it is polynomially related to the recent upper bound of [Andoni-Indyk-Krauthgamer, SODA'09]. From a technical perspective, we prove a direct-sum theorem for sketching product metrics that is of independent interest. We show that, for any metric X that requires sketch size which is a sufficiently large constant, sketching the max-product metric ld∞(X) requires Ω(d) bits. The conclusion, in fact, also holds for arbitrary two-way communication. The proof uses a novel technique for information complexity based on Poincaré inequalities and suggests an intimate connection between non-embeddability, sketching and communication complexity.