Equi-depth multidimensional histograms
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
Statistical profile estimation in database systems
ACM Computing Surveys (CSUR)
On the propagation of errors in the size of join results
SIGMOD '91 Proceedings of the 1991 ACM SIGMOD international conference on Management of data
Optimal histograms for limiting worst-case error propagation in the size of join results
ACM Transactions on Database Systems (TODS)
Balancing histogram optimality and practicality for query result size estimation
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Access path selection in a relational database management system
SIGMOD '79 Proceedings of the 1979 ACM SIGMOD international conference on Management of data
Estimating block transfers and join sizes
SIGMOD '83 Proceedings of the 1983 ACM SIGMOD international conference on Management of data
Accurate estimation of the number of tuples satisfying a condition
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Universality of Serial Histograms
VLDB '93 Proceedings of the 19th International Conference on Very Large Data Bases
The optimization of queries in relational databases
The optimization of queries in relational databases
A new histogram method for sparse attributes: the averaged rectangular attribute cardinality map
ISICT '03 Proceedings of the 1st international symposium on Information and communication technologies
A formal analysis of why heuristic functions work
Artificial Intelligence
A formal analysis of why heuristic functions work
Artificial Intelligence
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Current database systems utilize histograms to approximate frequency distributions of attribute values of relations. These are used to efficiently estimate query result sizes and access plan costs. Even though they have been in use for nearly two decades, there has been no significant mathematical techniques (other than those used in statistics for traditional histogram approximations) to study them. In this paper, we introduce a new histogram-like approximation strategy, called the Rectangular Attribute Cardinality Map (R-ACM), that aims to approximate the density of the underlying attribute values using the philosophies of numerical integration.In this new histogram-like approximation method, the density function within a given sector is approximated by a rectangular cell, where the height of the cell is obtained so as to guarantee that the actual probability density differs from the approximated one by a maximum of a user-specified tolerance, _ . Furthermore, unlike the two traditional histogram types, namely equi-width and equi-depth, the R-ACM is neither equi-width nor equi-depth. Analytically, we show that for the R-ACM, the distribution of an attribute value within the sector is Binomially distributed.This permits us to derive worst-case and average-case results for the estimation errors of the probability mass itself. Our theoretical results, which include a rigorous maximum likelihood and expected-case analyses, and an extensive set of experiments demonstrate that the R-ACM scheme (which is essentially histogram-like) is much more accurate than the traditional histograms for query result size estimation. Due to its high accuracy and low construction costs, we hope that it could become an invaluable tool for query optimization in the future database systems.