A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Automatic text processing
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Reporting points in halfspaces
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Vector quantization and signal compression
Vector quantization and signal compression
Ray shooting and parametric search
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Point location in arrangements of hyperplanes
Information and Computation
An algorithm for approximate closest-point queries
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Lower bounds for union-split-find related problems on random access machines
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Fuzzy queries in multimedia database systems
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
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
Determinism versus non-determinism for linear time RAMs (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Dimensionality reduction techniques for proximity problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Shape Indexing Using Approximate Nearest-Neighbour Search in High-Dimensional Spaces
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Time-Space Tradeoffs for Branching Programs
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A Non-Linear Time Lower Bound for Boolean Branching Programs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The cell probe complexity of succinct data structures
Theoretical Computer Science
ACM Transactions on Computation Theory (TOCT)
Unifying the Landscape of Cell-Probe Lower Bounds
SIAM Journal on Computing
Hi-index | 0.00 |
We prove new lower bounds for nearest neighbor search in the Hamming cube. Our lower bounds are for randomized, two-sided error, algorithms in Yao's cell probe model. Our bounds are in the form of a tradeoff among the number of cells, the size of a cell, and the search time. For example, suppose we are searching among n points in the d dimensional cube, we use poly(n, d) cells, each containing poly(d, log n) bits. We get a lower bound of Ω(d/log n) on the search time, a significant improvement over the recent bound of Ω(log d) of Borodin et al. This should be contrasted with the upper bound of O(log log d) for approximate search (and O(1) for a decision version of the problem; our lower bounds hold in that case). By previous results, the bounds for the cube imply similar bounds for nearest neighbor search in high dimensional Euclidean space, and for other geometric problems.