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Charting the tractability frontier of certain conjunctive query answering

Published:22 June 2013Publication History

ABSTRACT

An uncertain database is defined as a relational database in which primary keys need not be satisfied. A repair (or possible world) of such database is obtained by selecting a maximal number of tuples without ever selecting two distinct tuples with the same primary key value. For a Boolean query q, the decision problem CERTAINTY(q) takes as input an uncertain database db and asks whether q is satisfied by every repair of db. Our main focus is on acyclic Boolean conjunctive queries without self-join. Previous work has introduced the notion of (directed) attack graph of such queries, and has proved that CERTAINTY(q) is first-order expressible if and only if the attack graph of q is acyclic. The current paper investigates the boundary between tractability and intractability of CERTAINTY(q). We first classify cycles in attack graphs as either weak or strong, and then prove among others the following. If the attack graph of a query q contains a strong cycle, then CERTAINTY(q) is coNP-complete. If the attack graph of q contains no strong cycle and every weak cycle is terminal (i.e., no edge leads from a vertex in the cycle to a vertex outside the cycle), then CERTAINTY(q) is in P. We then partially address the only remaining open case, i.e., when the attack graph contains some nonterminal cycle and no strong cycle. Finally, we establish a relationship between the complexities of CERTAINTY(q) and evaluating q on probabilistic databases.

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      • Published in

        cover image ACM Conferences
        PODS '13: Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems
        June 2013
        334 pages
        ISBN:9781450320665
        DOI:10.1145/2463664
        • General Chair:
        • Richard Hull,
        • Program Chair:
        • Wenfei Fan

        Copyright © 2013 ACM

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 22 June 2013

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        PODS '13 Paper Acceptance Rate24of97submissions,25%Overall Acceptance Rate476of1,835submissions,26%

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