28,887 research outputs found
Domination parameters with number 2: interrelations and algorithmic consequences
In this paper, we study the most basic domination invariants in graphs, in
which number 2 is intrinsic part of their definitions. We classify them upon
three criteria, two of which give the following previously studied invariants:
the weak -domination number, , the -domination number,
, the -domination number, , the double
domination number, , the total -domination number,
, and the total double domination number, , where is a graph in which a corresponding invariant is well
defined. The third criterion yields rainbow versions of the mentioned six
parameters, one of which has already been well studied, and three other give
new interesting parameters. Together with a special, extensively studied Roman
domination, , and two classical parameters, the domination number,
, and the total domination number, , we consider 13
domination invariants in graphs . In the main result of the paper we present
sharp upper and lower bounds of each of the invariants in terms of every other
invariant, large majority of which are new results proven in this paper. As a
consequence of the main theorem we obtain some complexity results for the
studied invariants, in particular regarding the existence of approximation
algorithms and inapproximability bounds.Comment: 45 pages, 4 tables, 7 figure
Domination parameters with number 2: Interrelations and algorithmic consequences
In this paper, we study the most basic domination invariants in graphs, in which number 2 is intrinsic part of their definitions. We classify them upon three criteria, two of which give the following previously studied invariants: the weak 2-domination number, γw2(G), the 2-domination number, γ2(G), the {2}-domination number, γ{2}(G), the double domination number, γ×2(G), the total {2}-domination number, γt{2}(G), and the total double domination number, γt×2(G), where G is a graph in which the corresponding invariant is well defined. The third criterion yields rainbow versions of the mentioned six parameters, one of which has already been well studied, and three other give new interesting parameters. Together with a special, extensively studied Roman domination, γR(G), and two classical parameters, the domination number, γ(G), and the total domination number, γt(G), we consider 13 domination invariants in graphs. In the main result of the paper we present sharp upper and lower bounds of each of the invariants in terms of every other invariant, a large majority of which are new results proven in this paper. As a consequence of the main theorem we obtain new complexity results regarding the existence of approximation algorithms for the studied invariants, matched with tight or almost tight inapproximability bounds, which hold even in the class of split graphs.Fil: Bonomo, Flavia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Brešar, Boštjan. Institute of Mathematics, Physics and Mechanics; Eslovenia. University of Maribor; EsloveniaFil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Milanič, Martin. University of Primorska; EsloveniaFil: Safe, Martin Dario. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentin
Quantifying the reheating temperature of the universe
The aim of this paper is to determine an exact definition of the reheat
temperature for a generic perturbative decay of the inflaton. In order to
estimate the reheat temperature, there are two important conditions one needs
to satisfy: (a) the decay products of the inflaton must dominate the energy
density of the universe, i.e. the universe becomes completely radiation
dominated, and (b) the decay products of the inflaton have attained local
thermodynamical equilibrium. For some choices of parameters, the latter is a
more stringent condition, such that the decay products may thermalise much
after the beginning of radiation-domination. Consequently, we have obtained
that the reheat temperature can be much lower than the standard-lore
estimation. In this paper we describe under what conditions our universe could
have efficient or inefficient thermalisation, and quantify the reheat
temperature for both the scenarios. This result has an immediate impact on many
applications which rely on the thermal history of the universe, in particular
gravitino abundance.Comment: Discussion improved. New section added. Version matches the one
accepted for publicatio
Data Reductions and Combinatorial Bounds for Improved Approximation Algorithms
Kernelization algorithms in the context of Parameterized Complexity are often
based on a combination of reduction rules and combinatorial insights. We will
expose in this paper a similar strategy for obtaining polynomial-time
approximation algorithms. Our method features the use of
approximation-preserving reductions, akin to the notion of parameterized
reductions. We exemplify this method to obtain the currently best approximation
algorithms for \textsc{Harmless Set}, \textsc{Differential} and
\textsc{Multiple Nonblocker}, all of them can be considered in the context of
securing networks or information propagation
Massive neutrinos and cosmology
The present experimental results on neutrino flavour oscillations provide
evidence for non-zero neutrino masses, but give no hint on their absolute mass
scale, which is the target of beta decay and neutrinoless double-beta decay
experiments. Crucial complementary information on neutrino masses can be
obtained from the analysis of data on cosmological observables, such as the
anisotropies of the cosmic microwave background or the distribution of
large-scale structure. In this review we describe in detail how free-streaming
massive neutrinos affect the evolution of cosmological perturbations. We
summarize the current bounds on the sum of neutrino masses that can be derived
from various combinations of cosmological data, including the most recent
analysis by the WMAP team. We also discuss how future cosmological experiments
are expected to be sensitive to neutrino masses well into the sub-eV range.Comment: 122 pages, 23 figures, misprints corrected and references added.
Review article to be published in Physics Report
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