Size and treewidth bounds for conjunctive queries

  • Authors:

  • Georg Gottlob;Stephanie Tien Lee;Gregory J. Valiant

  • Affiliations:

  • Computing Laboratory and Oxford Man Institute of Quantitative Finance, University of Oxford, Oxford, United Kingdom;Computing Laboratory, University of Oxford, Oxford, United Kingdom;UC Berkeley, Berkeley, CA, USA

  • Venue:
  • Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
  • Year:
  • 2009

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Abstract

This paper provides new worst-case bounds for the size and treewith of the result Q(D) of a conjunctive query Q to a database D. We derive bounds for the result size |Q(D)| in terms of structural properties of Q, both in the absence and in the presence of keys and functional dependencies. These bounds are based on a novel "coloring" of the query variables that associates a coloring number C(Q) to each query Q. Using this coloring number, we derive tight bounds for the size of Q(D) in case (i) no functional dependencies or keys are specified, and (ii) simple (one-attribute) keys are given. These results generalize recent size-bounds for join queries obtained by Atserias, Grohe, and Marx (FOCS 2008). An extension of our coloring technique also gives a lower bound for |Q(D)| in the general setting of a query with arbitrary functional dependencies. Our new coloring scheme also allows us to precisely characterize (both in the absence of keys and with simple keys) the treewidth-preserving queries--the queries for which the output treewidth is bounded by a function of the input treewidth. Finally we characterize the queries that preserve the sparsity of the input in the general setting with arbitrary functional dependencies.