Equi-depth multidimensional histograms
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
Balancing histogram optimality and practicality for query result size estimation
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Improved histograms for selectivity estimation of range predicates
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Approximate medians and other quantiles in one pass and with limited memory
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Wavelet-based histograms for selectivity estimation
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Online computation and competitive analysis
Online computation and competitive analysis
The Aqua approximate query answering system
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Synopsis data structures for massive data sets
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Progressive vector transmission
Proceedings of the 7th ACM international symposium on Advances in geographic information systems
Optimal histograms for hierarchical range queries (extended abstract)
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Optimal and approximate computation of summary statistics for range aggregates
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Fast algorithms for hierarchical range histogram construction
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
Dynamic multidimensional histograms
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Wavelet synopses with error guarantees
Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Locally adaptive dimensionality reduction for indexing large time series databases
ACM Transactions on Database Systems (TODS)
Access path selection in a relational database management system
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
An Approximate L1-Difference Algorithm for Massive Data Streams
SIAM Journal on Computing
Optimal Histograms with Quality Guarantees
VLDB '98 Proceedings of the 24rd International Conference on Very Large Data Bases
Universality of Serial Histograms
VLDB '93 Proceedings of the 19th International Conference on Very Large Data Bases
Histogramming Data Streams with Fast Per-Item Processing
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximating a Data Stream for Querying and Estimation: Algorithms and Performance Evaluation
ICDE '02 Proceedings of the 18th International Conference on Data Engineering
Probabilistic wavelet synopses
ACM Transactions on Database Systems (TODS)
Space efficiency in synopsis construction algorithms
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Approximation algorithms for wavelet transform coding of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The history of histograms (abridged)
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
REHIST: relative error histogram construction algorithms
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
A Note on Linear Time Algorithms for Maximum Error Histograms
IEEE Transactions on Knowledge and Data Engineering
Efficient Process of Top-k Range-Sum Queries over Multiple Streams with Minimized Global Error
IEEE Transactions on Knowledge and Data Engineering
Deterministic algorithms for sampling count data
Data & Knowledge Engineering
Declaring independence via the sketching of sketches
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Hierarchical synopses with optimal error guarantees
ACM Transactions on Database Systems (TODS)
The VLDB Journal — The International Journal on Very Large Data Bases
A framework for estimating complex probability density structures in data streams
Proceedings of the 17th ACM conference on Information and knowledge management
Tight results for clustering and summarizing data streams
Proceedings of the 12th International Conference on Database Theory
Multiplicative synopses for relative-error metrics
Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology
Pseudo Period Detection on Time Series Stream with Scale Smoothing
APWeb/WAIM '09 Proceedings of the Joint International Conferences on Advances in Data and Web Management
Frequent pattern mining with uncertain data
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning from Data Streams: Synopsis and Change Detection
Proceedings of the 2008 conference on STAIRS 2008: Proceedings of the Fourth Starting AI Researchers' Symposium
Fast and effective histogram construction
Proceedings of the 18th ACM conference on Information and knowledge management
Probabilistic histograms for probabilistic data
Proceedings of the VLDB Endowment
Optimality and scalability in lattice histogram construction
Proceedings of the VLDB Endowment
Consistent histograms in the presence of distinct value counts
Proceedings of the VLDB Endowment
A Streaming Parallel Decision Tree Algorithm
The Journal of Machine Learning Research
Journal of Intelligent Information Systems
Approximating sliding windows by cyclic tree-like histograms for efficient range queries
Data & Knowledge Engineering
Approximation algorithms for speeding up dynamic programming and denoising aCGH data
Journal of Experimental Algorithmics (JEA)
Efficient construction of histograms for multidimensional data using quad-trees
Decision Support Systems
Distributed similarity estimation using derived dimensions
The VLDB Journal — The International Journal on Very Large Data Bases
Approximate dynamic programming using halfspace queries and multiscale Monge decomposition
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Monitoring incremental histogram distribution for change detection in data streams
Sensor-KDD'08 Proceedings of the Second international conference on Knowledge Discovery from Sensor Data
Graph sketches: sparsification, spanners, and subgraphs
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Approximating and testing k-histogram distributions in sub-linear time
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches
Foundations and Trends in Databases
Unexpected challenges in large scale machine learning
Proceedings of the 1st International Workshop on Big Data, Streams and Heterogeneous Source Mining: Algorithms, Systems, Programming Models and Applications
Histograms as statistical estimators for aggregate queries
Information Systems
Quality and efficiency for kernel density estimates in large data
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
Efficient and scalable monitoring and summarization of large probabilistic data
Proceedings of the 2013 Sigmod/PODS Ph.D. symposium on PhD symposium
Entropy-based histograms for selectivity estimation
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Differentially private histogram publication
The VLDB Journal — The International Journal on Very Large Data Bases
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Histograms and related synopsis structures are popular techniques for approximating data distributions. These have been successful in query optimization and a variety of applications, including approximate querying, similarity searching, and data mining, to name a few. Histograms were a few of the earliest synopsis structures proposed and continue to be used widely. The histogram construction problem is to construct the best histogram restricted to a space bound that reflects the data distribution most accurately under a given error measure.The histograms are used as quick and easy estimates. Thus, a slight loss of accuracy, compared to the optimal histogram under the given error measure, can be offset by fast histogram construction algorithms. A natural question arises in this context: Can we find a fast near optimal approximation algorithm for the histogram construction problem? In this article, we give the first linear time (1+ε)-factor approximation algorithms (for any ε 0) for a large number of histogram construction problems including the use of piecewise small degree polynomials to approximate data, workloads, etc. Several of our algorithms extend to data streams.Using synthetic and real-life data sets, we demonstrate that in many scenarios the approximate histograms are almost identical to optimal histograms in quality and are significantly faster to construct.