6,622 research outputs found
Structural Decompositions for Problems with Global Constraints
A wide range of problems can be modelled as constraint satisfaction problems
(CSPs), that is, a set of constraints that must be satisfied simultaneously.
Constraints can either be represented extensionally, by explicitly listing
allowed combinations of values, or implicitly, by special-purpose algorithms
provided by a solver.
Such implicitly represented constraints, known as global constraints, are
widely used; indeed, they are one of the key reasons for the success of
constraint programming in solving real-world problems. In recent years, a
variety of restrictions on the structure of CSP instances have been shown to
yield tractable classes of CSPs. However, most such restrictions fail to
guarantee tractability for CSPs with global constraints. We therefore study the
applicability of structural restrictions to instances with such constraints.
We show that when the number of solutions to a CSP instance is bounded in key
parts of the problem, structural restrictions can be used to derive new
tractable classes. Furthermore, we show that this result extends to
combinations of instances drawn from known tractable classes, as well as to CSP
instances where constraints assign costs to satisfying assignments.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/s10601-015-9181-
Exchangeable Variable Models
A sequence of random variables is exchangeable if its joint distribution is
invariant under variable permutations. We introduce exchangeable variable
models (EVMs) as a novel class of probabilistic models whose basic building
blocks are partially exchangeable sequences, a generalization of exchangeable
sequences. We prove that a family of tractable EVMs is optimal under zero-one
loss for a large class of functions, including parity and threshold functions,
and strictly subsumes existing tractable independence-based model families.
Extensive experiments show that EVMs outperform state of the art classifiers
such as SVMs and probabilistic models which are solely based on independence
assumptions.Comment: ICML 201
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
Tractability of multivariate analytic problems
In the theory of tractability of multivariate problems one usually studies
problems with finite smoothness. Then we want to know which -variate
problems can be approximated to within by using, say,
polynomially many in and function values or arbitrary
linear functionals.
There is a recent stream of work for multivariate analytic problems for which
we want to answer the usual tractability questions with
replaced by . In this vein of research, multivariate
integration and approximation have been studied over Korobov spaces with
exponentially fast decaying Fourier coefficients. This is work of J. Dick, G.
Larcher, and the authors. There is a natural need to analyze more general
analytic problems defined over more general spaces and obtain tractability
results in terms of and .
The goal of this paper is to survey the existing results, present some new
results, and propose further questions for the study of tractability of
multivariate analytic questions
Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges
Computational Social Choice is an interdisciplinary research area involving
Economics, Political Science, and Social Science on the one side, and
Mathematics and Computer Science (including Artificial Intelligence and
Multiagent Systems) on the other side. Typical computational problems studied
in this field include the vulnerability of voting procedures against attacks,
or preference aggregation in multi-agent systems. Parameterized Algorithmics is
a subfield of Theoretical Computer Science seeking to exploit meaningful
problem-specific parameters in order to identify tractable special cases of in
general computationally hard problems. In this paper, we propose nine of our
favorite research challenges concerning the parameterized complexity of
problems appearing in this context
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