Let's Play Tag: Linear Time Evaluation of Conjunctive Queries under TGD Constraints

TL;DR

This paper investigates the potential for linear-time evaluation of conjunctive queries under tuple-generating dependencies (TGDs), proposing methods to extend known dichotomies to certain classes of constraints and evaluation modes.

Contribution

It introduces an approach that extends dichotomy results to specific classes of TGDs and evaluation modes, advancing understanding of query evaluation complexity under constraints.

Findings

Applicable to non-recursive TGDs with binary head relations or two frontier variables

Effective for all evaluation modes except enumeration under certain TGD classes

Highlights challenges in enumeration and less restrictive TGD classes

Abstract

We study the limits of linear time evaluation of conjunctive queries under constraints expressed as tuple-generating dependencies (TGDs), across several modes of query evaluation: single-testing, all-testing, counting, lexicographic direct access, and enumeration. While full classifications seem far beyond reach, we propose an approach that, for some evaluation modes and classes of TGDs, makes it possible to lift known dichotomies from the unconstrained setting. In particular, our approach applies to all mentioned evaluation modes except enumeration, when the constraints fall into one of two classes: non-recursive sets of TGDs in which every TGD uses at most binary relation symbols in the head or has at most two frontier variables; and frontier-guarded full TGDs. We further provide a collection of examples showcasing the challenges that arise for enumeration and for less restrictive classes of TGDs.