Abstract

Random sampling is a standard technique for constructing (approximate) histograms for query optimization. However, any real implementation in commercial products requires solving the hard problem of determining "How much sampling is enough?" We address this critical question in the context of equi-height histograms used in many commercial products, including Microsoft SQL Server. We introduce a conservative error metric capturing the intuition that for an approximate histogram to have low error, the error must be small in all regions of the histogram. We then present a result establishing an optimal bound on the amount of sampling required for pre-specified error bounds. We also describe an adaptive page sampling algorithm which achieves greater efficiency by using all values in a sampled page but adjusts the amount of sampling depending on clustering of values in pages. Next, we establish that the problem of estimating the number of distinct values is provably difficult, but propose ...

Citations