A Dichotomy on the Complexity of Consistent Query Answering for Atoms with Simple Keys

TL;DR

This paper proves a conjecture that the complexity of consistent query answering for certain conjunctive queries is either polynomial-time solvable or coNP-complete, establishing a clear dichotomy for queries with simple keys.

Contribution

It confirms the existence of a complexity dichotomy for CERTAINTY(Q) in conjunctive queries without self-joins with simple or full keys.

Findings

The complexity of CERTAINTY(Q) is either in PTIME or coNP-complete.

The dichotomy holds for conjunctive queries without self-joins with simple or full keys.

The paper provides a complete classification of these query complexities.

Abstract

We study the problem of consistent query answering under primary key violations. In this setting, the relations in a database violate the key constraints and we are interested in maximal subsets of the database that satisfy the constraints, which we call repairs. For a boolean query Q, the problem CERTAINTY(Q) asks whether every such repair satisfies the query or not; the problem is known to be always in coNP for conjunctive queries. However, there are queries for which it can be solved in polynomial time. It has been conjectured that there exists a dichotomy on the complexity of CERTAINTY(Q) for conjunctive queries: it is either in PTIME or coNP-complete. In this paper, we prove that the conjecture is indeed true for the case of conjunctive queries without self-joins, where each atom has as a key either a single attribute (simple key) or all attributes of the atom.