Abstract
Single-round multiway join algorithms first reshuffle data over many servers and then evaluate the query at hand in a parallel and communication-free way. A key question is whether a given distribution policy for the reshuffle is adequate for computing a given query, also referred to as parallel-correctness. This article extends the study of the complexity of parallel-correctness and its constituents, parallel-soundness and parallel-completeness, to unions of conjunctive queries with negation. As a by-product, it is shown that the containment problem for conjunctive queries with negation is coNEXPTIME-complete.
Highlights
Motivated by recent in-memory systems like Spark [7] and Shark [21], Koutris and Suciu introduced the massively parallel communication model (MPC) [15] where computation proceeds in a sequence of parallel steps each followed by global synchronisation of all servers
As union and negation are fundamental operators, we extend in this paper the study of parallel-correctness to unions of conjunctive queries (UCQ), conjunctive queries with negation (CQ¬) and unions of conjunctive queries with negation (UCQ¬)
We obtained that deciding parallel-correctness for unions of conjunctive queries remains in Πp2, while the analog problem in the presence of negation is hard for coNEXPTIME
Summary
Motivated by recent in-memory systems like Spark [7] and Shark [21], Koutris and Suciu introduced the massively parallel communication model (MPC) [15] where computation proceeds in a sequence of parallel steps each followed by global synchronisation of all servers. Parallel-Correctness and Containment for CQs with Union and Negation parallel-correctness for conjunctive queries (CQs) is ΠP2 -complete under arbitrary distribution policies. Parallel-correctness (and its variants) for (unions of) conjunctive queries with negation is complete for coNEXPTIME. The complexity decreases from coNEXPTIME to Πp2 if the database schema is fixed or the arity of relations is bounded, and to coNP for unions of full conjunctive queries with negation. In the latter case, we again employ a reduction from containment of full conjunctive queries (with negation) and obtain novel results on the containment problem in this setting as well. Missing proof details can be found in the full version of this paper [14]
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