The complexity of acyclic conjunctive queries

  • Authors:

  • Georg Gottlob;Nicola Leone;Francesco Scarcello

  • Affiliations:

  • Technische Universität Wien, Vienna, Austria;University of Calabria, Rende, Italy;University of Calabria, Rende, Italy

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2001

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Abstract

This paper deals with the evaluation of acyclic Booleanconjunctive queries in relational databases. By well-known resultsof Yannakakis[1981], this problem is solvable in polynomial time;its precise complexity, however, has not been pinpointed so far. Weshow that the problem of evaluating acyclic Boolean conjunctivequeries is complete for LOGCFL, the class of decision problems thatare logspace-reducible to a context-free language. Since LOGCFL iscontained in AC1 and NC2, the evaluation problem of acyclic Booleanconjunctive queries is highly parallelizable. We present a paralleldatabase algorithm solving this problem with alogarithmic number ofparallel join operations. The algorithm is generalized to computingthe output of relevant classes of non-Boolean queries. We also showthat the acyclic versions of the following well-known database andAI problems are all LOGCFL-complete: The Query Output Tuple problemfor conjunctive queries, Conjunctive Query Containment, ClauseSubsumption, and Constraint Satisfaction. The LOGCFL-completenessresult is extended to the class of queries of bounded tree widthand to other relevant query classes which are more general than theacyclic queries.