Consistent Answers of Conjunctive Queries on Graphs

TL;DR

This paper investigates the computational complexity of obtaining consistent answers for Boolean conjunctive queries on directed graphs with a single binary relation, revealing a dichotomy between first-order expressibility and polynomial-time solvability.

Contribution

It extends prior work by analyzing conjunctive queries involving a single binary relation, establishing a clear complexity dichotomy for consistent answer computation.

Findings

Either the problem is first-order expressible or polynomial-time solvable.

Provides a complete classification for queries on directed graphs with a single binary relation.

Advances understanding of query answering under key constraints in graph databases.

Abstract

During the past decade, there has been an extensive investigation of the computational complexity of the consistent answers of Boolean conjunctive queries under primary key constraints. Much of this investigation has focused on self-join-free Boolean conjunctive queries. In this paper, we study the consistent answers of Boolean conjunctive queries involving a single binary relation, i.e., we consider arbitrary Boolean conjunctive queries on directed graphs. In the presence of a single key constraint, we show that for each such Boolean conjunctive query, either the problem of computing its consistent answers is expressible in first-order logic, or it is polynomial-time solvable, but not expressible in first-order logic.