Parameterised Complexity of Consistent Query Answering via Graph Representations

TL;DR

This paper explores the parameterized complexity of consistent query answering using graph representations, introducing new algorithms and theoretical results for counting repairs and analyzing complexity.

Contribution

It introduces solution-conflict hypergraphs and applies Courcelle's theorem to establish fixed-parameter tractability results for complex query answering.

Findings

Algorithm for counting repairs based on hypergraph tree decomposition.

Fixed-parameter tractability results for data complexity.

Fixed-parameter tractability results for combined complexity.

Abstract

We study consistent query answering via different graph representations. First, we introduce solution-conflict hypergraphs in which nodes represent facts and edges represent either conflicts or query solutions. Considering a monotonic query and a set of antimonotonic constraints, we present an explicit algorithm for counting the number of repairs satisfying the query based on a tree decomposition of the solution-conflict hypergraph. The algorithm not only provides fixed-parameter tractability results for data complexity over expressive query and constraint classes, but also introduces a novel and potentially implementable approach to repair counting. Second, we consider the Gaifman graphs arising from MSO descriptions of consistent query answering. Using a generalization of Courcelle's theorem, we then present fixed-parameter tractability results for combined complexity over expressive query and constraint classes.