Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Informatik

Fachvortrag Dr. Christoph Berkholz

  • Wann 13.02.2017 von 16:15 bis 23:59
  • Wo RUD 25, Humboldt-Kabinett
  • iCal

Fachvortrag von Herrn Dr. Christoph Berkholz (HU Berlin) zum Thema "Answering Conjunctive Queries under Updates".
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Abstract:

In this talk I present a recent joint work with Jens Keppeler and Nicole Schweikardt on the algorithmic task of answering conjunctive queries on dynamic databases. Our main result is a dichotomy theorem that precisely characterises those conjunctive queries that can be evaluated efficiently.
This work will appear at PODS 2017 and the more detailed abstract of the paper can be found below.
We consider the task of enumerating and counting answers to k-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear delay and sublinear update time (and arbitrary preprocessing time) is impossible.
For Boolean conjunctive queries and the more general problem of counting the number of solutions of a k-ary query we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time.
All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis.