Worst-Case Optimal Algorithms for Parallel Query Processing

TL;DR

This paper introduces worst-case optimal parallel algorithms for conjunctive query processing, defining a new query complexity measure and connecting parallel computation with external memory models to improve efficiency.

Contribution

It presents the first worst-case optimal parallel algorithms for conjunctive queries, introduces the edge quasi-packing number, and links parallel algorithms to external memory models for broader applicability.

Findings

Optimal load for single-round queries is O(M/p^{1/ψ*})

Algorithms are optimal for several classes of queries in multiple rounds

Connection to external memory models enables translation of parallel algorithms to I/O-efficient algorithms

Abstract

In this paper, we study the communication complexity for the problem of computing a conjunctive query on a large database in a parallel setting with $p$ servers. In contrast to previous work, where upper and lower bounds on the communication were specified for particular structures of data (either data without skew, or data with specific types of skew), in this work we focus on worst-case analysis of the communication cost. The goal is to find worst-case optimal parallel algorithms, similar to the work of [18] for sequential algorithms. We first show that for a single round we can obtain an optimal worst-case algorithm. The optimal load for a conjunctive query $q$ when all relations have size equal to $M$ is $O(M/p^{1/\psi^*})$, where $\psi^*$ is a new query-related quantity called the edge quasi-packing number, which is different from both the edge packing number and edge cover number of the query hypergraph. For multiple rounds, we present algorithms that are optimal for several classes of queries. Finally, we show a surprising connection to the external memory model, which allows us to translate parallel algorithms to external memory algorithms. This technique allows us to recover (within a polylogarithmic factor) several recent results on the I/O complexity for computing join queries, and also obtain optimal algorithms for other classes of queries.