487 research outputs found
Symmetric Weighted First-Order Model Counting
The FO Model Counting problem (FOMC) is the following: given a sentence
in FO and a number , compute the number of models of over a
domain of size ; the Weighted variant (WFOMC) generalizes the problem by
associating a weight to each tuple and defining the weight of a model to be the
product of weights of its tuples. In this paper we study the complexity of the
symmetric WFOMC, where all tuples of a given relation have the same weight. Our
motivation comes from an important application, inference in Knowledge Bases
with soft constraints, like Markov Logic Networks, but the problem is also of
independent theoretical interest. We study both the data complexity, and the
combined complexity of FOMC and WFOMC. For the data complexity we prove the
existence of an FO formula for which FOMC is #P-complete, and the
existence of a Conjunctive Query for which WFOMC is #P-complete. We also
prove that all -acyclic queries have polynomial time data complexity.
For the combined complexity, we prove that, for every fragment FO, , the combined complexity of FOMC (or WFOMC) is #P-complete.Comment: To appear at PODS'1
Conjunctive Queries on Probabilistic Graphs: The Limits of Approximability
Query evaluation over probabilistic databases is a notoriously intractable
problem -- not only in combined complexity, but for many natural queries in
data complexity as well. This motivates the study of probabilistic query
evaluation through the lens of approximation algorithms, and particularly of
combined FPRASes, whose runtime is polynomial in both the query and instance
size. In this paper, we focus on tuple-independent probabilistic databases over
binary signatures, which can be equivalently viewed as probabilistic graphs. We
study in which cases we can devise combined FPRASes for probabilistic query
evaluation in this setting.
We settle the complexity of this problem for a variety of query and instance
classes, by proving both approximability and (conditional) inapproximability
results. This allows us to deduce many corollaries of possible independent
interest. For example, we show how the results of Arenas et al. on counting
fixed-length strings accepted by an NFA imply the existence of an FPRAS for the
two-terminal network reliability problem on directed acyclic graphs: this was
an open problem until now. We also show that one cannot extend the recent
result of van Bremen and Meel that gives a combined FPRAS for self-join-free
conjunctive queries of bounded hypertree width on probabilistic databases:
neither the bounded-hypertree-width condition nor the self-join-freeness
hypothesis can be relaxed. Finally, we complement all our inapproximability
results with unconditional lower bounds, showing that DNNF provenance circuits
must have at least moderately exponential size in combined complexity.Comment: 19 pages. Submitte
Compressed Representations of Conjunctive Query Results
Relational queries, and in particular join queries, often generate large
output results when executed over a huge dataset. In such cases, it is often
infeasible to store the whole materialized output if we plan to reuse it
further down a data processing pipeline. Motivated by this problem, we study
the construction of space-efficient compressed representations of the output of
conjunctive queries, with the goal of supporting the efficient access of the
intermediate compressed result for a given access pattern. In particular, we
initiate the study of an important tradeoff: minimizing the space necessary to
store the compressed result, versus minimizing the answer time and delay for an
access request over the result. Our main contribution is a novel parameterized
data structure, which can be tuned to trade off space for answer time. The
tradeoff allows us to control the space requirement of the data structure
precisely, and depends both on the structure of the query and the access
pattern. We show how we can use the data structure in conjunction with query
decomposition techniques, in order to efficiently represent the outputs for
several classes of conjunctive queries.Comment: To appear in PODS'18; 35 pages; comments welcom
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