广义超树分解上的聚集
Aggregations over Generalized Hypertree Decompositions
摘要：
我们研究了一类聚合连接查询与多个聚合运算符评估的注释关系。我们表明，标准多路连接算法和广义超树分解（GHD）的直接扩展提供了最著名的运行时保证。相比之下，先前的工作使用定制的算法和数据结构，并且不匹配这些保证。我们对标准技术的扩展是一对简单的测试，（1）确定聚合算子的两个排序是否等价，（2）确定GHD是否与给定的排序兼容。这些测试提供了一种找到最佳GHD的方法，当提供给标准连接算法时，将正确回答给定的聚合连接查询。我们的第二类贡献是（1）等价于给定序的序集和（2）相容于某个等价序的GHD集的一对完全刻画。我们通过例子表明，以前的方法是不完整的。我们的特征的关键技术后果是一个兼容的GHD分解成一组（较小的）{ \em无约束} GHD，即成一组GHD的子查询没有聚合。由于这种分解是由不受约束的GHD，我们能够连接到GHD连接查询处理的广泛文献，从而获得改进的运行时边界，MapReduce变体，并找到近似最优GHD的有效方法。
英文摘要：
We study a class of aggregate-join queries with multiple aggregation operators evaluated over annotated relations. We show that straightforward extensions of standard multiway join algorithms and generalized hypertree decompositions (GHDs) provide best-known runtime guarantees. In contrast, prior work uses bespoke algorithms and data structures and does not match these guarantees. Our extensions to the standard techniques are a pair of simple tests that (1) determine if two orderings of aggregation operators are equivalent and (2) determine if a GHD is compatible with a given ordering. These tests provide a means to find an optimal GHD that, when provided to standard join algorithms, will correctly answer a given aggregate-join query. The second class of our contributions is a pair of complete characterizations of (1) the set of orderings equivalent to a given ordering and (2) the set of GHDs compatible with some equivalent ordering. We show by example that previous approaches are incomplete. The key technical consequence of our characterizations is a decomposition of a compatible GHD into a set of (smaller) {\em unconstrained} GHDs, i.e. into a set of GHDs of sub-queries without aggregations. Since this decomposition is comprised of unconstrained GHDs, we are able to connect to the wide literature on GHDs for join query processing, thereby obtaining improved runtime bounds, MapReduce variants, and an efficient method to find approximately optimal GHDs.
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