29,853 research outputs found
First-order query evaluation on structures of bounded degree
We consider the enumeration problem of first-order queries over structures of
bounded degree. It was shown that this problem is in the Constant-Delaylin
class. An enumeration problem belongs to Constant-Delaylin if for an input of
size n it can be solved by: - an O(n) precomputation phase building an index
structure, - followed by a phase enumerating the answers with no repetition and
a constant delay between two consecutive outputs. In this article we give a
different proof of this result based on Gaifman's locality theorem for
first-order logic. Moreover, the constants we obtain yield a total evaluation
time that is triply exponential in the size of the input formula, matching the
complexity of the best known evaluation algorithms
First-Order Query Evaluation with Cardinality Conditions
We study an extension of first-order logic that allows to express cardinality
conditions in a similar way as SQL's COUNT operator. The corresponding logic
FOC(P) was introduced by Kuske and Schweikardt (LICS'17), who showed that query
evaluation for this logic is fixed-parameter tractable on classes of structures
(or databases) of bounded degree. In the present paper, we first show that the
fixed-parameter tractability of FOC(P) cannot even be generalised to very
simple classes of structures of unbounded degree such as unranked trees or
strings with a linear order relation.
Then we identify a fragment FOC1(P) of FOC(P) which is still sufficiently
strong to express standard applications of SQL's COUNT operator. Our main
result shows that query evaluation for FOC1(P) is fixed-parameter tractable
with almost linear running time on nowhere dense classes of structures. As a
corollary, we also obtain a fixed-parameter tractable algorithm for counting
the number of tuples satisfying a query over nowhere dense classes of
structures
gMark: Schema-Driven Generation of Graphs and Queries
Massive graph data sets are pervasive in contemporary application domains.
Hence, graph database systems are becoming increasingly important. In the
experimental study of these systems, it is vital that the research community
has shared solutions for the generation of database instances and query
workloads having predictable and controllable properties. In this paper, we
present the design and engineering principles of gMark, a domain- and query
language-independent graph instance and query workload generator. A core
contribution of gMark is its ability to target and control the diversity of
properties of both the generated instances and the generated workloads coupled
to these instances. Further novelties include support for regular path queries,
a fundamental graph query paradigm, and schema-driven selectivity estimation of
queries, a key feature in controlling workload chokepoints. We illustrate the
flexibility and practical usability of gMark by showcasing the framework's
capabilities in generating high quality graphs and workloads, and its ability
to encode user-defined schemas across a variety of application domains.Comment: Accepted in November 2016. URL:
http://ieeexplore.ieee.org/document/7762945/. in IEEE Transactions on
Knowledge and Data Engineering 201
On Range Searching with Semialgebraic Sets II
Let be a set of points in . We present a linear-size data
structure for answering range queries on with constant-complexity
semialgebraic sets as ranges, in time close to . It essentially
matches the performance of similar structures for simplex range searching, and,
for , significantly improves earlier solutions by the first two authors
obtained in~1994. This almost settles a long-standing open problem in range
searching.
The data structure is based on the polynomial-partitioning technique of Guth
and Katz [arXiv:1011.4105], which shows that for a parameter , , there exists a -variate polynomial of degree such that
each connected component of contains at most points
of , where is the zero set of . We present an efficient randomized
algorithm for computing such a polynomial partition, which is of independent
interest and is likely to have additional applications
Dynamic Complexity of Parity Exists Queries
Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other or even all queries that are definable in first-order logic extended by parity quantifiers? We consider the query that asks whether the number of nodes that have an edge to a red node is odd. Already this simple query of quantifier structure parity-exists is a major roadblock for dynamically capturing extensions of first-order logic.
We show that this query cannot be maintained with quantifier-free first-order update rules, and that variants induce a hierarchy for such update rules with respect to the arity of the maintained auxiliary relations. Towards maintaining the query with full first-order update rules, it is shown that degree-restricted variants can be maintained
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
Challenges for Efficient Query Evaluation on Structured Probabilistic Data
Query answering over probabilistic data is an important task but is generally
intractable. However, a new approach for this problem has recently been
proposed, based on structural decompositions of input databases, following,
e.g., tree decompositions. This paper presents a vision for a database
management system for probabilistic data built following this structural
approach. We review our existing and ongoing work on this topic and highlight
many theoretical and practical challenges that remain to be addressed.Comment: 9 pages, 1 figure, 23 references. Accepted for publication at SUM
201
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