Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
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
Approximations and optimal geometric divide-and-conquer
Selected papers of the 23rd annual ACM symposium on Theory of computing
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
Improved bounds on the sample complexity of learning
Journal of Computer and System Sciences
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Learning in Neural Networks: Theoretical Foundations
Learning in Neural Networks: Theoretical Foundations
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Tight Error Bounds of Geometric Problems on Convex Objects with Imprecise Coordinates
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating extent measures of points
Journal of the ACM (JACM)
Indexing multi-dimensional uncertain data with arbitrary probability density functions
VLDB '05 Proceedings of the 31st international conference on Very large data bases
OLAP over uncertain and imprecise data
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Estimating statistical aggregates on probabilistic data streams
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Efficient aggregation algorithms for probabilistic data
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient query evaluation on probabilistic databases
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Efficient indexing methods for probabilistic threshold queries over uncertain data
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Algorithms for ε-Approximations of Terrains
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Triangulating input-constrained planar point sets
Information Processing Letters
Probabilistic Threshold Range Aggregate Query Processing over Uncertain Data
APWeb/WAIM '09 Proceedings of the Joint International Conferences on Advances in Data and Web Management
Histograms and Wavelets on Probabilistic Data
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Semantics of Ranking Queries for Probabilistic Data and Expected Ranks
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Small and stable descriptors of distributions for geometric statistical problems
Small and stable descriptors of distributions for geometric statistical problems
Representing uncertain data: models, properties, and algorithms
The VLDB Journal — The International Journal on Very Large Data Bases
Largest bounding box, smallest diameter, and related problems on imprecise points
Computational Geometry: Theory and Applications
Stochastic minimum spanning trees in euclidean spaces
Proceedings of the twenty-seventh annual symposium on Computational geometry
Geometric Approximation Algorithms
Geometric Approximation Algorithms
Efficient Computation of Range Aggregates against Uncertain Location-Based Queries
IEEE Transactions on Knowledge and Data Engineering
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We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a subset of the uncertain points, including their locational uncertainty, so that range counting queries can be answered by just examining this subset. We study three distinct types of queries. RE queries return the expected number of points in a query range. RC queries return the number of points in the range with probability at least a threshold. RQ queries returns the probability that fewer than some threshold fraction of the points are in the range. In both RC and RQ coresets the threshold is provided as part of the query. And for each type of query we provide coreset constructions with approximation-size tradeoffs. We show that random sampling can be used to construct each type of coreset, and we also provide significantly improved bounds using discrepancy-based approaches on axis-aligned range queries.