199 research outputs found
On Sparsification for Computing Treewidth
We investigate whether an n-vertex instance (G,k) of Treewidth, asking
whether the graph G has treewidth at most k, can efficiently be made sparse
without changing its answer. By giving a special form of OR-cross-composition,
we prove that this is unlikely: if there is an e > 0 and a polynomial-time
algorithm that reduces n-vertex Treewidth instances to equivalent instances, of
an arbitrary problem, with O(n^{2-e}) bits, then NP is in coNP/poly and the
polynomial hierarchy collapses to its third level.
Our sparsification lower bound has implications for structural
parameterizations of Treewidth: parameterizations by measures that do not
exceed the vertex count, cannot have kernels with O(k^{2-e}) bits for any e >
0, unless NP is in coNP/poly. Motivated by the question of determining the
optimal kernel size for Treewidth parameterized by vertex cover, we improve the
O(k^3)-vertex kernel from Bodlaender et al. (STACS 2011) to a kernel with
O(k^2) vertices. Our improved kernel is based on a novel form of
treewidth-invariant set. We use the q-expansion lemma of Fomin et al. (STACS
2011) to find such sets efficiently in graphs whose vertex count is
superquadratic in their vertex cover number.Comment: 21 pages. Full version of the extended abstract presented at IPEC
201
Microcanonical Treatment of Hadronizing the Quark-Gluon Plasma
We recently introduced a completely new way to study ultrarelativistic
nuclear scattering by providing a link between the string model approach and a
statistical description. A key issue is the microcanonical treatment of
hadronizing individual quark matter droplets. In this paper we describe in
detail the hadronization of these droplets according to n-body phase space, by
using methods of statistical physics, i.e. constructing Markov chains of hadron
configurations.Comment: Complete paper enclosed as postscript file (uuencoded
Scattering of first and second sound waves by quantum vorticity in superfluid Helium
We study the scattering of first and second sound waves by quantum vorticity
in superfluid Helium using two-fluid hydrodynamics. The vorticity of the
superfluid component and the sound interact because of the nonlinear character
of these equations. Explicit expressions for the scattered pressure and
temperature are worked out in a first Born approximation, and care is exercised
in delimiting the range of validity of the assumptions needed for this
approximation to hold. An incident second sound wave will partly convert into
first sound, and an incident first sound wave will partly convert into second
sound. General considerations show that most incident first sound converts into
second sound, but not the other way around. These considerations are validated
using a vortex dipole as an explicitely worked out example.Comment: 24 pages, Latex, to appear in Journal of Low Temperature Physic
A Testpart for Interdisciplinary Analyses in Micro Production Engineering
AbstractIn 2011, a round robin test was initiated within the group of CIRP Research Affiliates. The aim was to establish a platform for linking interdisciplinary research in order to share the expertise and experiences of participants all over the world. This paper introduces a testpart which has been designed to allow an analysis of different manufacturing technologies, simulation methods, machinery and metrology as well as process and production planning aspects. Current investigations are presented focusing on the machining and additive processes to produce the geometry, simulation approaches, machine analysis, and a comparison of measuring technologies. Challenges and limitations regarding the manufacturing and evaluation of the testpart features by the applied methods are discussed.Video abstrac
Terrestrial Implications of Cosmological Gamma-Ray Burst Models
The observation by the BATSE instrument on the Compton Gamma Ray Observatory
that gamma-ray bursts (GRBs) are distributed isotropically around the Earth but
nonuniformly in distance has led to the widespread conclusion that GRBs are
most likely to be at cosmological distances, making them the most luminous
sources known in the Universe. If bursts arise from events that occur in normal
galaxies, such as neutron star binary inspirals, then they will also occur in
our Galaxy about every hundred thousand to million years. The gamma-ray flux at
the Earth due to a Galactic GRB would far exceed that from even the largest
solar flares. The absorption of this radiation in the atmosphere would
substantially increase the stratospheric nitric oxide concentration through
photodissociation of N, greatly reducing the ozone concentration for
several years through NO catalysis, with important biospheric effects due
to increased solar ultraviolet flux. A nearby GRB may also leave traces in
anomalous radionuclide abundances.Comment: uuencoded, gzip-ed postscript; 6 pages; submitted to ApJ Letter
On a Clique-Based Integer Programming Formulation of Vertex Colouring with Applications in Course Timetabling
Vertex colouring is a well-known problem in combinatorial optimisation, whose
alternative integer programming formulations have recently attracted
considerable attention. This paper briefly surveys seven known formulations of
vertex colouring and introduces a formulation of vertex colouring using a
suitable clique partition of the graph. This formulation is applicable in
timetabling applications, where such a clique partition of the conflict graph
is given implicitly. In contrast with some alternatives, the presented
formulation can also be easily extended to accommodate complex performance
indicators (``soft constraints'') imposed in a number of real-life course
timetabling applications. Its performance depends on the quality of the clique
partition, but encouraging empirical results for the Udine Course Timetabling
problem are reported
Subregion graph: A path planning acceleration structure for characters with various motion types in very large environments
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