Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
A lower bound on the complexity of approximate nearest-neighbor searching on the Hamming cube
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Lower bounds for high dimensional nearest neighbor search and related problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Tighter bounds for nearest neighbor search and related problems in the cell probe model
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On approximate nearest neighbors under I norm
Journal of Computer and System Sciences
A strong lower bound for approximate nearest neighbor searching
Information Processing Letters
An Optimal Randomised Cell Probe Lower Bound for Approximate Nearest Neighbour Searching
FOCS '04 Proceedings of the 45th 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
On the Optimality of the Dimensionality Reduction Method
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Higher Lower Bounds for Near-Neighbor and Further Rich Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
Communications of the ACM - 50th anniversary issue: 1958 - 2008
Earth mover distance over high-dimensional spaces
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A Geometric Approach to Lower Bounds for Approximate Near-Neighbor Search and Partial Match
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Hardness of Nearest Neighbor under L-infinity
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Lower Bounds on Near Neighbor Search via Metric Expansion
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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We give new lower bounds for randomized NNS data structures in the cell probe model based on robust metric expansion for two metric spaces: l∞ and Earth Mover Distance (EMD) in high dimensions. In particular, our results imply stronger non-embedability for these metric spaces into l1. The main components of our approach are a strengthening of the isoperimetric inequality for the distribution on l∞ introduced by Andoni et al [FOCS'08] and a robust isoperimetric inequality for EMD on quotients of the boolean hypercube.