The fine classification of conjunctive queries and parameterized logarithmic space

Chen, Hubie and Muller, M. (2015) The fine classification of conjunctive queries and parameterized logarithmic space. In: UNSPECIFIED (ed.) PODS '13 Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems. New York, U.S.: ACM Publications, pp. 309-320. ISBN 9781450320665.

Abstract

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.

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