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 OUT (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.

翻译：我们提出了一种新方法，用于估计大型数据库D中小连接查询Q的答案数量OUT，并进行连接上的均匀采样。我们的方法是首个满足以下所有条件的方法：- 支持任意Q，包括无环或有环查询，并包含二元和非二元关系。- 保证在 ~O(AGM/OUT) 时间内以高概率实现任意小的误差，其中AGM是AGM界OUT（OUT的一个上界），~O 隐藏了输入规模的多对数因子。我们还在一个统一框架中解释了先前的连接大小估计方法。包括我们的方法在内的所有方法都依赖于D中关系上的特定索引，这些索引离线构建时间为线性。此外，我们利用广义超树分解（GHDs）扩展了方法，在OUT较小时实现了低于 ~O(AGM/OUT) 的复杂度，并提出了提高估计效率和准确性的优化技术。