Exact and Approximate Counting of Database Repairs

TL;DR

This paper extends the classification of counting database repairs from primary keys to general functional dependencies, analyzing exact and approximate counting complexities, and identifying cases where approximation is feasible.

Contribution

It generalizes existing results to functional dependencies, introduces new complexity classifications, and identifies specific FD classes where approximation is possible.

Findings

Counting repairs for primary keys and CQs is FP/#P-complete.

Approximate counting is always feasible for primary keys and CQs.

Approximation is intractable for general FDs, but feasible for FDs with left-hand side chains.

Abstract

A key task in the context of consistent query answering is to count the number of repairs that entail the query, with the ultimate goal being a precise data complexity classification. This has been achieved in the case of primary keys and self-join-free conjunctive queries (CQs) via an FP/#P-complete dichotomy. We lift this result to the more general case of functional dependencies (FDs). Another important task in this context is whenever the counting problem in question is intractable, to classify it as approximable, i.e., the target value can be efficiently approximated with error guarantees via a fully polynomial-time randomized approximation scheme (FPRAS), or as inapproximable. Although for primary keys and CQs (even with self-joins) the problem is always approximable, we prove that this is not the case for FDs. We show, however, that the class of FDs with a left-hand side chain forms an island of approximability. We see these results, apart from being interesting in their own right, as crucial steps towards a complete classification of approximate counting of repairs in the case of FDs and self-join-free CQs.