21 research outputs found
Kernelization and Sparseness: the case of Dominating Set
We prove that for every positive integer and for every graph class
of bounded expansion, the -Dominating Set problem admits a
linear kernel on graphs from . Moreover, when is only
assumed to be nowhere dense, then we give an almost linear kernel on for the classic Dominating Set problem, i.e., for the case . These
results generalize a line of previous research on finding linear kernels for
Dominating Set and -Dominating Set. However, the approach taken in this
work, which is based on the theory of sparse graphs, is radically different and
conceptually much simpler than the previous approaches.
We complement our findings by showing that for the closely related Connected
Dominating Set problem, the existence of such kernelization algorithms is
unlikely, even though the problem is known to admit a linear kernel on
-topological-minor-free graphs. Also, we prove that for any somewhere dense
class , there is some for which -Dominating Set is
W[]-hard on . Thus, our results fall short of proving a sharp
dichotomy for the parameterized complexity of -Dominating Set on
subgraph-monotone graph classes: we conjecture that the border of tractability
lies exactly between nowhere dense and somewhere dense graph classes.Comment: v2: new author, added results for r-Dominating Sets in bounded
expansion graph
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Sting jets in intense winter North-Atlantic windstorms
Extratropical cyclones dominate autumn and winter weather over
western Europe. The strongest cyclones, often termed windstorms, have
a large socio-economic impact due to the strong surface winds and
associated storm surges in coastal areas. Here we show that sting jets
are a common feature of windstorms; up to a third of the 100 most
intense North Atlantic winter windstorms over the last two decades satisfy
conditions for sting jets. The sting jet is a mesoscale descending
airstream that can cause strong near-surface winds in the dry slot of
the cyclone, a region not usually associated with strong
winds. Despite their localized transient nature these sting jets can
cause significant damage, a prominent example being the storm that
devastated southeast England on 16 October 1987. We present the first
regional climatology of windstorms with sting jets. Previously
analysed sting jet cases appear to have been exceptional in their
track over northwest Europe rather than in their strength
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A comparison of two identification and tracking methods for polar lows
In this study, we compare two different cyclone-tracking algorithms to detect North Atlantic polar lows, which
are very intense mesoscale cyclones. Both approaches include spatial filtering, detection, tracking and
constraints specific to polar lows. The first method uses digital bandpass-filtered mean sea level pressure
(MSLP) fieldsin the spatial range of 200ïżœ600 km and is especially designed for polar lows. The second method
also uses a bandpass filter but is based on the discrete cosine transforms (DCT) and can be applied to MSLP
and vorticity fields. The latter was originally designed for cyclones in general and has been adapted to polar
lows for this study. Both algorithms are applied to the same regional climate model output fields from October
1993 to September 1995 produced from dynamical downscaling of the NCEP/NCAR reanalysis data.
Comparisons between these two methods show that different filters lead to different numbers and locations of
tracks. The DCT is more precise in scale separation than the digital filter and the results of this study suggest
that it is more suited for the bandpass filtering of MSLP fields. The detection and tracking parts also influence
the numbers of tracks although less critically. After a selection process that applies criteria to identify tracks of
potential polar lows, differences between both methods are still visible though the major systems are identified
in both
A c k n 5-Approximation Algorithm for Treewidth
We give an algorithm that for an input n-vertex graph G and integer k> 0, in time O(c k n) either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k + 4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single-exponential in k and linear in n. Treewidth based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single-exponential in the treewidth and linear in the input size
A cÎșn 5-Approximation algorithm for treewidth
We give an algorithm that for an input n-vertex graph G and integer Îș > 0, in time 2O(Îș)n, either outputs that the treewidth of G is larger than Îș, or gives a tree decomposition of G of width at most 5Îș + 4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in Îș and linear in n. Treewidth-based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single exponential in the treewidth and linear in the input size
A c\u3csup\u3eÎș\u3c/sup\u3en 5-Approximation algorithm for treewidth
\u3cp\u3eWe give an algorithm that for an input n-vertex graph G and integer Îș > 0, in time 2\u3csup\u3eO(Îș)\u3c/sup\u3en, either outputs that the treewidth of G is larger than Îș, or gives a tree decomposition of G of width at most 5Îș + 4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in Îș and linear in n. Treewidth-based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single exponential in the treewidth and linear in the input size.\u3c/p\u3
A cÎșn 5-Approximation algorithm for treewidth
We give an algorithm that for an input n-vertex graph G and integer Îș > 0, in time 2O(Îș)n, either outputs that the treewidth of G is larger than Îș, or gives a tree decomposition of G of width at most 5Îș + 4. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in Îș and linear in n. Treewidth-based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single exponential in the treewidth and linear in the input size