Equi-depth multidimensional histograms
SIGMOD '88 Proceedings of the 1988 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
Practical algorithms for self scaling histograms or better than average data collection
Performance Evaluation
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
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
Maintaining Stream Statistics over Sliding Windows
SIAM Journal on Computing
Accurate estimation of the number of tuples satisfying a condition
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Fast Incremental Maintenance of Approximate Histograms
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
Continuously Maintaining Quantile Summaries of the Most Recent N Elements over a Data Stream
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Effective Computation of Biased Quantiles over Data Streams
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Approximate counts and quantiles over sliding windows
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Space-efficient Relative Error Order Sketch over Data Streams
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Space- and time-efficient deterministic algorithms for biased quantiles over data streams
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A Fast Algorithm for Approximate Quantiles in High Speed Data Streams
SSDBM '07 Proceedings of the 19th International Conference on Scientific and Statistical Database Management
How to summarize the universe: dynamic maintenance of quantiles
VLDB '02 Proceedings of the 28th international conference on Very Large Data Bases
The history of histograms (abridged)
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
An efficient algorithm for approximate biased quantile computation in data streams
Proceedings of the sixteenth ACM conference on Conference on information and knowledge management
Fast and accurate computation of equi-depth histograms over data streams
Proceedings of the 14th International Conference on Extending Database Technology
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Histograms provide effective synopses of large data sets, and are thus used in a wide variety of applications, including query optimization, approximate query answering, distribution fitting, parallel database partitioning, and data mining. Moreover, very fast approximate algorithms are needed to compute accurate histograms on fast-arriving data streams, whereby online queries can be supported within the given memory and computing resources. Many real-life applications require that the data distribution in certain regions must be modeled with greater accuracy, and Biased Histograms are designed to address this need. In this paper, we define biased histograms over data streams and sliding windows on data streams, and propose the Bar Splitting Biased Histogram (BSBH) algorithm to construct them efficiently and accurately. We prove that BSBH generates expected ∈-approximate biased histograms for data streams with stationary distributions, and our experiments show that BSBH also achieves good approximation in the presence of concept shifts, even major ones. Additionally, BSBH employs a new biased sampling technique which outperforms uniform sampling in terms of accuracy, while using about the same amount of time and memory. Therefore, BSBH outperforms previously proposed algorithms for computing biased histograms over the whole data stream, and it is the first algorithm that supports windows.