Evaluating Datalog over Semirings: A Grounding-based Approach

TL;DR

This paper introduces a two-phase framework for analyzing the data complexity of evaluating Datalog programs over semirings, providing tight runtime bounds and efficient algorithms for specific semiring classes.

Contribution

It presents a novel two-phase approach combining grounding and fixpoint evaluation, with algorithms tailored for finite-rank and absorptive semirings, achieving state-of-the-art results.

Findings

Developed algorithms for minimal grounding using structure-aware techniques.

Established efficient fixpoint algorithms for finite-rank and absorptive semirings.

Provided matching lower bounds for the evaluation complexity.

Abstract

Datalog is a powerful yet elegant language that allows expressing recursive computation. Although Datalog evaluation has been extensively studied in the literature, so far, only loose upper bounds are known on how fast a Datalog program can be evaluated. In this work, we ask the following question: given a Datalog program over a naturally-ordered semiring $\sigma$, what is the tightest possible runtime? To this end, our main contribution is a general two-phase framework for analyzing the data complexity of Datalog over $\sigma$: first ground the program into an equivalent system of polynomial equations (i.e. grounding) and then find the least fixpoint of the grounding over $\sigma$. We present algorithms that use structure-aware query evaluation techniques to obtain the smallest possible groundings. Next, efficient algorithms for fixpoint evaluation are introduced over two classes of semirings: (1) finite-rank semirings and (2) absorptive semirings of total order. Combining both phases, we obtain state-of-the-art and new algorithmic results. Finally, we complement our results with a matching fine-grained lower bound.