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arXiv · 2412.08324

Parameterised Complexity of Consistent Query Answering via Graph Representations

Teemu Hankala·Miika Hannula·Yasir Mahmood·Arne Meier
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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.

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Teemu Hankala, Miika Hannula, Yasir Mahmood, Arne Meier. 2024-12-11. Parameterised Complexity of Consistent Query Answering via Graph Representations. https://arxiv.org/abs/2412.08324

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