Factorised Representations of Query Results

TL;DR

This paper introduces a framework for analyzing query result tractability through factorised representations, which can be polynomial in size despite exponential result cardinality, by leveraging regularity and readability measures.

Contribution

It presents a novel approach to represent query results efficiently using factorisation, along with a characterization of select-project-join queries based on readability bounds and an algorithm to find optimal representations.

Findings

Factorised representations can be polynomial in size despite exponential result cardinality.

Readability measures the regularity of query results and guides efficient representations.

An algorithm is provided to compute asymptotically optimal factorised representations.

Abstract

Query tractability has been traditionally defined as a function of input database and query sizes, or of both input and output sizes, where the query result is represented as a bag of tuples. In this report, we introduce a framework that allows to investigate tractability beyond this setting. The key insight is that, although the cardinality of a query result can be exponential, its structure can be very regular and thus factorisable into a nested representation whose size is only polynomial in the size of both the input database and query. For a given query result, there may be several equivalent representations, and we quantify the regularity of the result by its readability, which is the minimum over all its representations of the maximum number of occurrences of any tuple in that representation. We give a characterisation of select-project-join queries based on the bounds on readability of their results for any input database. We complement it with an algorithm that can find asymptotically optimal upper bounds and corresponding factorised representations.