Work-Efficient Query Evaluation in Constant Time with PRAMs

TL;DR

This paper develops work-efficient algorithms for constant-time query evaluation on CRCW PRAMs, focusing on relational algebra queries and leveraging approximate prefix sums and compaction techniques.

Contribution

It introduces algorithms that achieve near-optimal work bounds for constant-time query evaluation under mild data assumptions.

Findings

Algorithms for relational operators in constant time with near-optimal work bounds.

Efficient evaluation for acyclic, semijoin, and join queries in specific settings.

Use of approximate prefix sums and compaction to achieve work efficiency.

Abstract

The article studies query evaluation in parallel constant time in the CRCW PRAM model. While it is well-known that all relational algebra queries can be evaluated in constant time on an appropriate CRCW PRAM model, this article is interested in the efficiency of evaluation algorithms, that is, in the number of processors or, asymptotically equivalent, in the work. Naive evaluation in the parallel setting results in huge (polynomial) bounds on the work of such algorithms and in presentations of the result sets that can be extremely scattered in memory. The article discusses some obstacles for constant-time PRAM query evaluation. It presents algorithms for relational operators and explores three settings, in which efficient sequential query evaluation algorithms exist: acyclic queries, semijoin algebra queries, and join queries -- the latter in the worst-case optimal framework. Under mild assumptions -- that data values are numbers of polynomial size in the size of the database or that the relations of the database are suitably sorted -- constant-time algorithms are presented that are weakly work-efficient in the sense that work $\mathcal{O}(T^{1+\varepsilon})$ can be achieved, for every $\varepsilon>0$, compared to the time $T$ of an optimal sequential algorithm. Important tools are the algorithms for approximate prefix sums and compaction from Goldberg and Zwick (1995).