Quantified Conjunctive Queries on Partially Ordered Sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8894)

Abstract

We study the computational problem of checking whether a quantified conjunctive query (a first-order sentence built using only conjunction as Boolean connective) is true in a finite poset (a reflexive, antisymmetric, and transitive directed graph). We prove that the problem is already \(\mathrm {NP}\)-hard on a certain fixed poset, and investigate structural properties of posets yielding fixed-parameter tractability when the problem is parameterized by the query. Our main algorithmic result is that model checking quantified conjunctive queries on posets of bounded width is fixed-parameter tractable (the width of a poset is the maximum size of a subset of pairwise incomparable elements). We complement our algorithmic result by complexity results with respect to classes of finite posets in a hierarchy of natural poset invariants, establishing its tightness in this sense.

Keywords

Quantified conjunctive queries Posets Parameterized complexity 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Vienna University of TechnologyViennaAustria

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