Exploiting ordered dictionaries to efficiently construct histograms with q-error guarantees in SAP HANA

Abstract

Histograms that guarantee a maximum multiplicative error (q-error) for estimates may significantly improve the plan quality of query optimizers. However, the construction time for histograms with maximum q-error was too high for practical use cases. In this paper we extend this concept with a threshold, i.e., an estimate or true cardinality θ, below which we do not care about the q-error because we still expect optimal plans. This allows us to develop far more efficient construction algorithms for histograms with bounded error. The test for θ, q-acceptability developed also exploits the order-preserving dictionary encoding of SAP HANA. We have integrated this family of histograms into SAP HANA, and we report on the construction time, histograms size, and estimation errors on real-world data sets. In virtually all cases the histograms can be constructed in far less than one second, requiring less than 5% of space compared to the original compressed data.