696 research outputs found
A Trichotomy in the Complexity of Counting Answers to Conjunctive Queries
Conjunctive queries are basic and heavily studied database queries; in
relational algebra, they are the select-project-join queries. In this article,
we study the fundamental problem of counting, given a conjunctive query and a
relational database, the number of answers to the query on the database. In
particular, we study the complexity of this problem relative to sets of
conjunctive queries. We present a trichotomy theorem, which shows essentially
that this problem on a set of conjunctive queries is either tractable,
equivalent to the parameterized CLIQUE problem, or as hard as the parameterized
counting CLIQUE problem; the criteria describing which of these situations
occurs is simply stated, in terms of graph-theoretic conditions
Counting Answers to Existential Positive Queries: A Complexity Classification
Existential positive formulas form a fragment of first-order logic that
includes and is semantically equivalent to unions of conjunctive queries, one
of the most important and well-studied classes of queries in database theory.
We consider the complexity of counting the number of answers to existential
positive formulas on finite structures and give a trichotomy theorem on query
classes, in the setting of bounded arity. This theorem generalizes and unifies
several known results on the complexity of conjunctive queries and unions of
conjunctive queries.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0719
Answering Conjunctive Queries under Updates
We consider the task of enumerating and counting answers to -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 answering Boolean conjunctive queries and for the more general problem of
counting the number of solutions of k-ary queries 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.
By sublinear we mean for some
, where is the size of the active domain of the current
database
The Logic of Counting Query Answers
We consider the problem of counting the number of answers to a first-order
formula on a finite structure. We present and study an extension of first-order
logic in which algorithms for this counting problem can be naturally and
conveniently expressed, in senses that are made precise and that are motivated
by the wish to understand tractable cases of the counting problem
Matching Dependencies with Arbitrary Attribute Values: Semantics, Query Answering and Integrity Constraints
Matching dependencies (MDs) were introduced to specify the identification or
matching of certain attribute values in pairs of database tuples when some
similarity conditions are satisfied. Their enforcement can be seen as a natural
generalization of entity resolution. In what we call the "pure case" of MDs,
any value from the underlying data domain can be used for the value in common
that does the matching. We investigate the semantics and properties of data
cleaning through the enforcement of matching dependencies for the pure case. We
characterize the intended clean instances and also the "clean answers" to
queries as those that are invariant under the cleaning process. The complexity
of computing clean instances and clean answers to queries is investigated.
Tractable and intractable cases depending on the MDs and queries are
identified. Finally, we establish connections with database "repairs" under
integrity constraints.Comment: 13 pages, double column, 2 figure
Structurally Tractable Uncertain Data
Many data management applications must deal with data which is uncertain,
incomplete, or noisy. However, on existing uncertain data representations, we
cannot tractably perform the important query evaluation tasks of determining
query possibility, certainty, or probability: these problems are hard on
arbitrary uncertain input instances. We thus ask whether we could restrict the
structure of uncertain data so as to guarantee the tractability of exact query
evaluation. We present our tractability results for tree and tree-like
uncertain data, and a vision for probabilistic rule reasoning. We also study
uncertainty about order, proposing a suitable representation, and study
uncertain data conditioned by additional observations.Comment: 11 pages, 1 figure, 1 table. To appear in SIGMOD/PODS PhD Symposium
201
Counting answers to unions of conjunctive queries: natural tractability criteria and meta-complexity
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