84 research outputs found
Paradigms for Parameterized Enumeration
The aim of the paper is to examine the computational complexity and
algorithmics of enumeration, the task to output all solutions of a given
problem, from the point of view of parameterized complexity. First we define
formally different notions of efficient enumeration in the context of
parameterized complexity. Second we show how different algorithmic paradigms
can be used in order to get parameter-efficient enumeration algorithms in a
number of examples. These paradigms use well-known principles from the design
of parameterized decision as well as enumeration techniques, like for instance
kernelization and self-reducibility. The concept of kernelization, in
particular, leads to a characterization of fixed-parameter tractable
enumeration problems.Comment: Accepted for MFCS 2013; long version of the pape
The complexity of satisfaction problems in reverse mathematics
Satisfiability problems play a central role in computer science and
engineering as a general framework for studying the complexity of various
problems. Schaefer proved in 1978 that truth satisfaction of propositional
formulas given a language of relations is either NP-complete or tractable. We
classify the corresponding satisfying assignment construction problems in the
framework of reverse mathematics and show that the principles are either
provable over RCA or equivalent to WKL. We formulate also a Ramseyan version of
the problems and state a different dichotomy theorem. However, the different
classes arising from this classification are not known to be distinct.Comment: 19 page
GRS 1915+105 : High-energy Insights with SPI/INTEGRAL
We report on results of two years of INTEGRAL/SPI monitoring of the Galactic
microquasar GRS 1915+105. From September 2004 to May 2006, the source has been
observed twenty times with long (approx 100 ks) exposures. We present an
analysis of the SPI data and focus on the description of the high-energy (> 20
keV) output of the source. We found that the 20 - 500 keV spectral emission of
GRS 1915+105 was bound between two states. It seems that these high-energy
states are not correlated with the temporal behavior of the source, suggesting
that there is no direct link between the macroscopic characteristics of the
coronal plasma and the the variability of the accretion flow. All spectra are
well fitted by a thermal comptonization component plus an extra high-energy
powerlaw. This confirms the presence of thermal and non-thermal electrons
around the black hole.Comment: 7 pages, 8 figures, 2 tables; accepted (09/11/2008) for publication
in A&
A Dichotomy Theorem for the Approximate Counting of Complex-Weighted Bounded-Degree Boolean CSPs
We determine the computational complexity of approximately counting the total
weight of variable assignments for every complex-weighted Boolean constraint
satisfaction problem (or CSP) with any number of additional unary (i.e., arity
1) constraints, particularly, when degrees of input instances are bounded from
above by a fixed constant. All degree-1 counting CSPs are obviously solvable in
polynomial time. When the instance's degree is more than two, we present a
dichotomy theorem that classifies all counting CSPs admitting free unary
constraints into exactly two categories. This classification theorem extends,
to complex-weighted problems, an earlier result on the approximation complexity
of unweighted counting Boolean CSPs of bounded degree. The framework of the
proof of our theorem is based on a theory of signature developed from Valiant's
holographic algorithms that can efficiently solve seemingly intractable
counting CSPs. Despite the use of arbitrary complex weight, our proof of the
classification theorem is rather elementary and intuitive due to an extensive
use of a novel notion of limited T-constructibility. For the remaining degree-2
problems, in contrast, they are as hard to approximate as Holant problems,
which are a generalization of counting CSPs.Comment: A4, 10pt, 20 pages. This revised version improves its preliminary
version published under a slightly different title in the Proceedings of the
4th International Conference on Combinatorial Optimization and Applications
(COCOA 2010), Lecture Notes in Computer Science, Springer, Vol.6508 (Part I),
pp.285--299, Kailua-Kona, Hawaii, USA, December 18--20, 201
Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems
For a finite set Gamma of Boolean relations, MAX ONES SAT(Gamma) and EXACT ONES SAT(Gamma) are generalized satisfiability problems where every constraint relation is from Gamma, and the task is to find a satisfying assignment with at least/exactly k variables set to 1, respectively. We study the parameterized complexity of these problems, including the question whether they admit polynomial kernels. For MAX ONES SAT(Gamma), we give a classification into five different complexity levels: polynomial-time solvable, admits a polynomial kernel, fixed-parameter tractable, solvable in polynomial time for fixed k, and NP-hard already for k = 1. For EXACT ONES SAT(Gamma), we refine the classification obtained earlier by taking a closer look at the fixed-parameter tractable cases and classifying the sets Gamma for which EXACT ONES SAT(Gamma) admits a polynomial kernel
Effect of antimicrobial use on the resistance of Escherichia coli in faecal flora of pigs
The antimicrobial use in veterinary medicine is of concern because of possible transmisston of resistant bacteria to humans. However the relation between use and occurrence of resistance is poorly documented in the field. Sixteen farrow-to-fimsh herds were selected and classified on the frequency of antimicrobial administrations (low (LU), medium (MU) and high (HU) users). lndtcative Eschenchia coli strains were tsolated from faeces of sows (5 per herd) and young pigs (3 per sow) at several ttmes during animals\u27 hfe and tested for reststance to amoxicillin, gentamicin, trimethoprim-sulfamids and tetracyclin. The percentages of resistant strams were compared between herd groups
Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis
Obtaining lower bounds for NP-hard problems has for a long time been an
active area of research. Recent algebraic techniques introduced by Jonsson et
al. (SODA 2013) show that the time complexity of the parameterized SAT()
problem correlates to the lattice of strong partial clones. With this ordering
they isolated a relation such that SAT() can be solved at least as fast
as any other NP-hard SAT() problem. In this paper we extend this method
and show that such languages also exist for the max ones problem
(MaxOnes()) and the Boolean valued constraint satisfaction problem over
finite-valued constraint languages (VCSP()). With the help of these
languages we relate MaxOnes and VCSP to the exponential time hypothesis in
several different ways.Comment: This is an extended version of Relating the Time Complexity of
Optimization Problems in Light of the Exponential-Time Hypothesis, appearing
in Proceedings of the 39th International Symposium on Mathematical
Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201
A Multivariate Approach for Checking Resiliency in Access Control
In recent years, several combinatorial problems were introduced in the area
of access control. Typically, such problems deal with an authorization policy,
seen as a relation , where means that
user is authorized to access resource . Li, Tripunitara and Wang (2009)
introduced the Resiliency Checking Problem (RCP), in which we are given an
authorization policy, a subset of resources , as well as
integers , and . It asks whether upon removal of
any set of at most users, there still exist pairwise disjoint sets of
at most users such that each set has collectively access to all resources
in . This problem possesses several parameters which appear to take small
values in practice. We thus analyze the parameterized complexity of RCP with
respect to these parameters, by considering all possible combinations of . In all but one case, we are able to settle whether the problem is in
FPT, XP, W[2]-hard, para-NP-hard or para-coNP-hard. We also consider the
restricted case where for which we determine the complexity for all
possible combinations of the parameters
On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions
The problem of deciding whether CSP instances admit solutions has been deeply
studied in the literature, and several structural tractability results have
been derived so far. However, constraint satisfaction comes in practice as a
computation problem where the focus is either on finding one solution, or on
enumerating all solutions, possibly projected to some given set of output
variables. The paper investigates the structural tractability of the problem of
enumerating (possibly projected) solutions, where tractability means here
computable with polynomial delay (WPD), since in general exponentially many
solutions may be computed. A general framework based on the notion of tree
projection of hypergraphs is considered, which generalizes all known
decomposition methods. Tractability results have been obtained both for classes
of structures where output variables are part of their specification, and for
classes of structures where computability WPD must be ensured for any possible
set of output variables. These results are shown to be tight, by exhibiting
dichotomies for classes of structures having bounded arity and where the tree
decomposition method is considered
Complexity transitions in global algorithms for sparse linear systems over finite fields
We study the computational complexity of a very basic problem, namely that of
finding solutions to a very large set of random linear equations in a finite
Galois Field modulo q. Using tools from statistical mechanics we are able to
identify phase transitions in the structure of the solution space and to
connect them to changes in performance of a global algorithm, namely Gaussian
elimination. Crossing phase boundaries produces a dramatic increase in memory
and CPU requirements necessary to the algorithms. In turn, this causes the
saturation of the upper bounds for the running time. We illustrate the results
on the specific problem of integer factorization, which is of central interest
for deciphering messages encrypted with the RSA cryptosystem.Comment: 23 pages, 8 figure
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