Faster methods for random sampling
Communications of the ACM
Random sampling with a reservoir
ACM Transactions on Mathematical Software (TOMS)
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
A guided tour of Chernoff bounds
Information Processing Letters
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
ACM Computing Surveys (CSUR)
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
Handbook of discrete and computational geometry
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Coresets in dynamic geometric data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sampling in dynamic data streams and applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Multi-pass geometric algorithms
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Deterministic sampling and range counting in geometric data streams
ACM Transactions on Algorithms (TALG)
Summarizing Two-Dimensional Data with Skyline-Based Statistical Descriptors
SSDBM '08 Proceedings of the 20th international conference on Scientific and Statistical Database Management
Comparing distributions and shapes using the kernel distance
Proceedings of the twenty-seventh annual symposium on Computational geometry
Monitoring continuous band-join queries over dynamic data
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Adaptive spatial partitioning for multidimensional data streams
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Density estimation for spatial data streams
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
Streaming algorithms for geometric problems
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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We consider the problem of approximate range counting over streams of d-dimensional points. In the data stream model, the algorithm makes a single scan of the data, which is presented in an arbitrary order, and computes a compact summary (called a sketch). The sketch, whose size depends on the approximation parameter ε, can be used to count the number of points inside a query range within additive error εn, where n is the size of the stream. We present several results, deterministic and randomized, for both rectangle and halfplane ranges.