14,251 research outputs found
Understanding the complexity of #SAT using knowledge compilation
Two main techniques have been used so far to solve the #P-hard problem #SAT.
The first one, used in practice, is based on an extension of DPLL for model
counting called exhaustive DPLL. The second approach, more theoretical,
exploits the structure of the input to compute the number of satisfying
assignments by usually using a dynamic programming scheme on a decomposition of
the formula. In this paper, we make a first step toward the separation of these
two techniques by exhibiting a family of formulas that can be solved in
polynomial time with the first technique but needs an exponential time with the
second one. We show this by observing that both techniques implicitely
construct a very specific boolean circuit equivalent to the input formula. We
then show that every beta-acyclic formula can be represented by a polynomial
size circuit corresponding to the first method and exhibit a family of
beta-acyclic formulas which cannot be represented by polynomial size circuits
corresponding to the second method. This result shed a new light on the
complexity of #SAT and related problems on beta-acyclic formulas. As a
byproduct, we give new handy tools to design algorithms on beta-acyclic
hypergraphs
Indeterministic Handling of Uncertain Decisions in Duplicate Detection
In current research, duplicate detection is usually considered as a deterministic approach in which tuples are either declared as duplicates or not. However, most often it is not completely clear whether two tuples represent the same real-world entity or not. In deterministic approaches, however, this uncertainty is ignored, which in turn can lead to false decisions. In this paper, we present an indeterministic approach for handling uncertain decisions in a duplicate detection process by using a probabilistic target schema. Thus, instead of deciding between multiple possible worlds, all these worlds can be modeled in the resulting data. This approach minimizes the negative impacts of false decisions. Furthermore, the duplicate detection process becomes almost fully automatic and human effort can be reduced to a large extent. Unfortunately, a full-indeterministic approach is by definition too expensive (in time as well as in storage) and hence impractical. For that reason, we additionally introduce several semi-indeterministic methods for heuristically reducing the set of indeterministic handled decisions in a meaningful way
Lattices with non-Shannon Inequalities
We study the existence or absence of non-Shannon inequalities for variables
that are related by functional dependencies. Although the power-set on four
variables is the smallest Boolean lattice with non-Shannon inequalities there
exist lattices with many more variables without non-Shannon inequalities. We
search for conditions that ensures that no non-Shannon inequalities exist. It
is demonstrated that 3-dimensional distributive lattices cannot have
non-Shannon inequalities and planar modular lattices cannot have non-Shannon
inequalities. The existence of non-Shannon inequalities is related to the
question of whether a lattice is isomorphic to a lattice of subgroups of a
group.Comment: Ten pages. Submitted to ISIT 2015. The appendix will not appear in
the proceeding
Human Motion Capture Data Tailored Transform Coding
Human motion capture (mocap) is a widely used technique for digitalizing
human movements. With growing usage, compressing mocap data has received
increasing attention, since compact data size enables efficient storage and
transmission. Our analysis shows that mocap data have some unique
characteristics that distinguish themselves from images and videos. Therefore,
directly borrowing image or video compression techniques, such as discrete
cosine transform, does not work well. In this paper, we propose a novel
mocap-tailored transform coding algorithm that takes advantage of these
features. Our algorithm segments the input mocap sequences into clips, which
are represented in 2D matrices. Then it computes a set of data-dependent
orthogonal bases to transform the matrices to frequency domain, in which the
transform coefficients have significantly less dependency. Finally, the
compression is obtained by entropy coding of the quantized coefficients and the
bases. Our method has low computational cost and can be easily extended to
compress mocap databases. It also requires neither training nor complicated
parameter setting. Experimental results demonstrate that the proposed scheme
significantly outperforms state-of-the-art algorithms in terms of compression
performance and speed
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
Provenance Circuits for Trees and Treelike Instances (Extended Version)
Query evaluation in monadic second-order logic (MSO) is tractable on trees
and treelike instances, even though it is hard for arbitrary instances. This
tractability result has been extended to several tasks related to query
evaluation, such as counting query results [3] or performing query evaluation
on probabilistic trees [10]. These are two examples of the more general problem
of computing augmented query output, that is referred to as provenance. This
article presents a provenance framework for trees and treelike instances, by
describing a linear-time construction of a circuit provenance representation
for MSO queries. We show how this provenance can be connected to the usual
definitions of semiring provenance on relational instances [20], even though we
compute it in an unusual way, using tree automata; we do so via intrinsic
definitions of provenance for general semirings, independent of the operational
details of query evaluation. We show applications of this provenance to capture
existing counting and probabilistic results on trees and treelike instances,
and give novel consequences for probability evaluation.Comment: 48 pages. Presented at ICALP'1
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