Consistently Estimating the Selectivity of Conjuncts of Predicates

Cost-based query optimizers need to estimate the selectivity of conjunctive predicates when comparing alternative query execution plans. To this end, advanced optimizers use multivariate statistics (MVS) to improve information about the joint distribution of attribute values in a table. The joint distribution for all columns is almost always too large to store completely, and the resulting use of partial distribution information raises the possibility that multiple, non-equivalent selectivity estimates may be available for a given predicate. Current optimizers use ad hoc methods to ensure that selectivities are estimated in a consistent manner. These methods ignore valuable information and tend to bias the optimizer toward query plans for which the least information is available, often yielding poor results. In this paper we present a novel method for consistent selectivity estimation based on the principle of maximum entropy (ME). Our method efficiently exploits all available information and avoids the bias problem. In the absence of detailed knowledge, the ME approach reduces to standard uniformity and independence assumptions. Our implementation using a prototype version of DB2 UDB shows that ME improves the optimizer's cardinality estimates by orders of magnitude, resulting in better plan quality and significantly reduced query execution times.