Covers of Query Results

TL;DR

This paper introduces covers, succinct lossless representations of query results based on minimal edge covers, enabling efficient computation and enumeration for various query types and applications.

Contribution

It develops a theoretical framework for covers using fractional hypertree decompositions and introduces a new operator, cover-join, for efficient computation and enumeration.

Findings

Covers can be computed in worst-case optimal time up to a logarithmic factor.

Enumeration from covers has linearithmic pre-computation and constant delay.

The framework generalizes to functional aggregate queries, impacting multiple computational domains.

Abstract

We introduce succinct lossless representations of query results called covers. They are subsets of the query results that correspond to minimal edge covers in the hypergraphs of these results. We first study covers whose structures are given by fractional hypertree decompositions of join queries. For any decomposition of a query, we give asymptotically tight size bounds for the covers of the query result over that decomposition and show that such covers can be computed in worst-case optimal time up to a logarithmic factor in the database size. For acyclic join queries, we can compute covers compositionally using query plans with a new operator called cover-join. The tuples in the query result can be enumerated from any of its covers with linearithmic pre-computation time and constant delay. We then generalize covers from joins to functional aggregate queries that express a host of computational problems such as aggregate-join queries, in-database optimization, matrix chain multiplication, and inference in probabilistic graphical models.