Guaranteeing the O(AGM/OUT) Runtime for Uniform Sampling and Size Estimation over Joins

Abstract

We propose a new method for estimating the number of answers OUT of a small join query 𝑄 in a large database 𝐷, and for uniform sampling over joins. Our method is the first to satisfy all the following statements. • Support arbitrary 𝑄, which can be either acyclic or cyclic, and contain binary and non-binary relations. • Guarantee an arbitrary small error with a high probability always in 𝑂˜(𝐴𝐺𝑀/OUT) time, where 𝐴𝐺𝑀 is the AGM bound (an upper bound of OUT), and 𝑂˜ hides the polylogarithmic factor of input size. We also explain previous join size estimators in a unified framework. All methods including ours rely on certain indexes on relations in 𝐷, which take linear time to build offline. Additionally, we extend our method using generalized hypertree decompositions (GHDs) to achieve a lower complexity than 𝑂˜ (𝐴𝐺𝑀/OUT) when OUT is small, and present optimization techniques for improving estimation efficiency and accuracy