Aggregations over Generalized Hypertree Decompositions

Recent multiway join algorithms have been shown to be asymptotically faster than any sequence of pairwise joins. Generalized Hypertree Decompositions (GHDs), introduced by Gottlob et al., provide a query plan for utilizing these multiway join algorithms to solve conjunctive queries. It is interesting to extend these new algorithms and query plans to more sophisticated queries, e.g. those including aggregations. Inspired by the semi-ring annotations of Green et al. and the query language of Abo Khamis et al., we study a class of queries involving aggregations and joins over annotated relations. Our queries are rich enough to capture traditional notions of queries with aggregations, e.g. group by aggregations in SQL, as well as a wide range of problems outside traditional data processing, e.g. message passing in graphical models. We then extend existing algorithms and structures to answer these queries. Our work has three primary contributions. First, we recover and improve the state of the art by placing a simple, easy to check condition on permissible GHDs. Second, we describe how to construct these “valid” GHDs by stitching together (ordinary) GHDs of a series of hypergraphs. This allows us to apply a series of existing research on GHDs, including some that provides strongest-known runtime guarantees for both serial and distributed join algorithm. Finally, we extend our problem to compute queries with multiple different aggregations, delving into and characterizing completely the details of how aggregations and joins can be reordered. 1998 ACM Subject Classification H.2.4 Database Management Systems