New upper bounds in Klee's measure problem
SIAM Journal on Computing
Computing a maximum axis-aligned rectangle in a convex polygon
Information Processing Letters
Exact and approximate aggregation in constraint query languages
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
On the complexity of computing the measure of ∪[ai,bi]
Communications of the ACM
Progressive approximate aggregate queries with a multi-resolution tree structure
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic multidimensional histograms
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
An introduction to spatial database systems
The VLDB Journal — The International Journal on Very Large Data Bases - Spatial Database Systems
Parametric Rectangles: A Model for Querying and Animation of Spatiotemporal Databases
EDBT '00 Proceedings of the 7th International Conference on Extending Database Technology: Advances in Database Technology
Surfing Wavelets on Streams: One-Pass Summaries for Approximate Aggregate Queries
Proceedings of the 27th International Conference on Very Large Data Bases
Finding Frequent Items in Data Streams
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Klee`s Measure Problem in Small Dimensions
SOFSEM '98 Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Efficient OLAP Operations in Spatial Data Warehouses
SSTD '01 Proceedings of the 7th International Symposium on Advances in Spatial and Temporal Databases
One-Pass Wavelet Decompositions of Data Streams
IEEE Transactions on Knowledge and Data Engineering
Approximate Aggregation Techniques for Sensor Databases
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximation techniques for spatial data
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Synopsis diffusion for robust aggregation in sensor networks
SenSys '04 Proceedings of the 2nd international conference on Embedded networked sensor systems
Range Aggregate Processing in Spatial Databases
IEEE Transactions on Knowledge and Data Engineering
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved range-summable random variable construction algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An improved data stream summary: the count-min sketch and its applications
Journal of Algorithms
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Cluster Hull: A Technique for Summarizing Spatial Data Streams
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Fast range-summable random variables for efficient aggregate estimation
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
An in-place algorithm for Klee's measure problem in two dimensions
Information Processing Letters
Range-Efficient Counting of Distinct Elements in a Massive Data Stream
SIAM Journal on Computing
On computing temporal aggregates with range predicates
ACM Transactions on Database Systems (TODS)
A (slightly) faster algorithm for klee's measure problem
Proceedings of the twenty-fourth annual symposium on Computational geometry
Two improved range-efficient algorithms for F0 estimation
Theoretical Computer Science
Proceedings of the forty-second ACM symposium on Theory of computing
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
New results on two-dimensional orthogonal range aggregation in external memory
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Streaming Algorithms via Precision Sampling
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Compressed matrix multiplication
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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We consider the estimation of aggregates over a data stream of multidimensional axis-aligned rectangles. Rectangles are a basic primitive object in spatial databases, and efficient aggregation of rectangles is a fundamental task. The data stream model has emerged as a de facto model for processing massive databases in which the data resides in external memory or the cloud and is streamed through main memory. For a point p, let n(p) denote the sum of the weights of all rectangles in the stream that contain p. We give near-optimal solutions for basic problems, including (1) the k-th frequency moment Fk = ∑ points p|n(p)|k, (2)~the counting version of stabbing queries, which seeks an estimate of n(p) given p, and (3) identification of heavy-hitters, i.e., points p for which n(p) is large. An important special case of Fk is F0, which corresponds to the volume of the union of the rectangles. This is a celebrated problem in computational geometry known as "Klee's measure problem", and our work yields the first solution in the streaming model for dimensions greater than one.