Robust regression and outlier detection
Robust regression and outlier detection
Computing a centerpoint of a finite planar set of points in linear time
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Approximations and optimal geometric divide-and-conquer
Selected papers of the 23rd annual ACM symposium on Theory of computing
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Maintaining stream statistics over sliding windows: (extended abstract)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computing location depth and regression depth in higher dimensions
Statistics and Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Better algorithms for high-dimensional proximity problems via asymmetric embeddings
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Iceberg Queries Efficiently
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Frequency Estimation of Internet Packet Streams with Limited Space
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A simple algorithm for finding frequent elements in streams and bags
ACM Transactions on Database Systems (TODS)
Sublinear geometric algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximate frequency counts over data streams
VLDB '02 Proceedings of the 28th international conference on Very Large Data Bases
Reverse nearest neighbor aggregates over data streams
VLDB '02 Proceedings of the 28th international conference on Very Large Data Bases
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
Sampling algorithms in a stream operator
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
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)
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Geometric streaming algorithms with a sorting primitive
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Monitoring continuous band-join queries over dynamic data
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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 present memory-efficient deterministic algorithms for constructing ∈-nets and ∈-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.