Conjunctive-query containment and constraint satisfaction
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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Theoretical Computer Science
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Journal of Computer and System Sciences
Complexity classifications of boolean constraint satisfaction problems
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When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
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Journal of the ACM (JACM)
Optimal implementation of conjunctive queries in relational data bases
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Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
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Journal of the ACM (JACM)
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Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
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Journal of Computer and System Sciences
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Algorithms and theory of computation handbook
On the space complexity of parameterized problems
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Parameterized Complexity
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We perform a fundamental investigation of the complexity of conjunctive query evaluation from the perspective of parameterized complexity. We classify sets of boolean conjunctive queries according to the complexity of this problem. Previous work showed that a set of conjunctive queries is fixed-parameter tractable precisely when the set is equivalent to a set of queries having bounded treewidth. We present a fine classification of query sets up to parameterized logarithmic space reduction. We show that, in the bounded treewidth regime, there are three complexity degrees and that the properties that determine the degree of a query set are bounded pathwidth and bounded tree depth. We also engage in a study of the two higher degrees via logarithmic space machine characterizations and complete problems. Our work yields a significantly richer perspective on the complexity of conjunctive queries and, at the same time, suggests new avenues of research in parameterized complexity.