Size Bound-Adorned Datalog

TL;DR

This paper introduces EDB-bounded datalog, a framework for deriving size bounds and complexity estimates for recursive datalog queries, enabling efficient evaluation and boundedness detection.

Contribution

It presents an algorithm to transform arbitrary datalog programs into EDB-bounded forms with size bounds and complexity analysis, including a semi-decision procedure for boundedness.

Findings

Provides polynomial size bounds for IDB predicates based on adornments.

Derives fixed-parameter tractable complexity bounds for query evaluation.

Offers an efficient semi-decision procedure for datalog boundedness.

Abstract

We introduce EDB-bounded datalog, a framework for deriving upper bounds on intermediate result sizes and the asymptotic complexity of recursive queries in datalog. We present an algorithm that, given an arbitrary datalog program, constructs an EDB-bounded datalog program in which every rule is adorned with a (non-recursive) conjunctive query that subsumes the result of the rule, thus acting as an upper bound. From such adornments, we define a notion of width based on (integral or fractional) edge-cover widths. Through the adornments and the width measure, we obtain, for every IDB predicate, worst-case upper bounds on their sizes, which are polynomial in the input data size, given a fixed program structure. Furthermore, with these size bounds, we also derive fixed-parameter tractable, output-sensitive asymptotic complexity bounds for evaluating the entire program. Additionally, by adapting our framework, we obtain a semi-decision procedure for datalog boundedness that efficiently rewrites most practical bounded programs into non-recursive equivalent programs.