Satisfiability algorithms for conjunctive queries over trees

  • Authors:
  • James Cheney

  • Affiliations:
  • LFCS, University of Edinburgh

  • Venue:
  • Proceedings of the 14th International Conference on Database Theory
  • Year:
  • 2011

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Abstract

We investigate the satisfiability problem for conjunctions of constraints over ordered, unranked trees, including child, descendant, following-sibling, root, leaf, and first/last child constraints. We introduce new, symbolic approaches based on graph transformations, which simplify and check the consistency of a problem first, and delay blind search as long as possible. We prove correctness and termination for these algorithms. We also analyze the complexity of important special cases: binary and κ-ary intersection of certain classes of XPath expressions. Our main complexity result is that binary intersection (for positive, simple navigational XPath over all axes) is tractable for expressions with a bounded number of changes in direction in the path, which is typically small.