110 research outputs found
Old Techniques for New Join Algorithms: A Case Study in RDF Processing
Recently there has been significant interest around designing specialized RDF
engines, as traditional query processing mechanisms incur orders of magnitude
performance gaps on many RDF workloads. At the same time researchers have
released new worst-case optimal join algorithms which can be asymptotically
better than the join algorithms in traditional engines. In this paper we apply
worst-case optimal join algorithms to a standard RDF workload, the LUBM
benchmark, for the first time. We do so using two worst-case optimal engines:
(1) LogicBlox, a commercial database engine, and (2) EmptyHeaded, our prototype
research engine with enhanced worst-case optimal join algorithms. We show that
without any added optimizations both LogicBlox and EmptyHeaded outperform two
state-of-the-art specialized RDF engines, RDF-3X and TripleBit, by up to 6x on
cyclic join queries-the queries where traditional optimizers are suboptimal. On
the remaining, less complex queries in the LUBM benchmark, we show that three
classic query optimization techniques enable EmptyHeaded to compete with RDF
engines, even when there is no asymptotic advantage to the worst-case optimal
approach. We validate that our design has merit as EmptyHeaded outperforms
MonetDB by three orders of magnitude and LogicBlox by two orders of magnitude,
while remaining within an order of magnitude of RDF-3X and TripleBit
Optimal Joins Using Compact Data Structures
Worst-case optimal join algorithms have gained a lot of attention in the database literature. We now count with several algorithms that are optimal in the worst case, and many of them have been implemented and validated in practice. However, the implementation of these algorithms often requires an enhanced indexing structure: to achieve optimality we either need to build completely new indexes, or we must populate the database with several instantiations of indexes such as B+-trees. Either way, this means spending an extra amount of storage space that may be non-negligible.
We show that optimal algorithms can be obtained directly from a representation that regards the relations as point sets in variable-dimensional grids, without the need of extra storage. Our representation is a compact quadtree for the static indexes, and a dynamic quadtree sharing subtrees (which we dub a qdag) for intermediate results. We develop a compositional algorithm to process full join queries under this representation, and show that the running time of this algorithm is worst-case optimal in data complexity. Remarkably, we can extend our framework to evaluate more expressive queries from relational algebra by introducing a lazy version of qdags (lqdags). Once again, we can show that the running time of our algorithms is worst-case optimal
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