5,296 research outputs found
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Dynamics of airflow in a short inhalation
During a rapid inhalation, such as a sniff, the flow in the airways
accelerates and decays quickly. The consequences for flow development and
convective trans- port of an inhaled gas were investigated in a subject
geometry extending from the nose to the bronchi. The progress of flow
transition and the advance of an inhaled non-absorbed gas were determined using
highly resolved simulations of a sniff 0.5 s long, 1 litre per second peak
flow, 364 ml inhaled volume. In the nose, the distribution of airflow evolved
through three phases: (i) an initial transient of about 50 ms, roughly the
filling time for a nasal volume, (ii) quasi-equilibrium over the majority of
the inhalation, and (iii) a terminating phase. Flow transition commenced in the
supraglottic region within 20ms, resulting in large- amplitude fluctuations
persisting throughout the inhalation; in the nose, fluctuations that arose
nearer peak flow were of much reduced intensity and diminished in the flow
decay phase. Measures of gas concentration showed non-uniform build-up and
wash-out of the inhaled gas in the nose. At the carina, the form of the
temporal concentration profile reflected both shear dispersion and airway
filling defects owing to recirculation regions.Comment: 15 page
Tree-based Coarsening and Partitioning of Complex Networks
Many applications produce massive complex networks whose analysis would
benefit from parallel processing. Parallel algorithms, in turn, often require a
suitable network partition. For solving optimization tasks such as graph
partitioning on large networks, multilevel methods are preferred in practice.
Yet, complex networks pose challenges to established multilevel algorithms, in
particular to their coarsening phase.
One way to specify a (recursive) coarsening of a graph is to rate its edges
and then contract the edges as prioritized by the rating. In this paper we (i)
define weights for the edges of a network that express the edges' importance
for connectivity, (ii) compute a minimum weight spanning tree with
respect to these weights, and (iii) rate the network edges based on the
conductance values of 's fundamental cuts. To this end, we also (iv)
develop the first optimal linear-time algorithm to compute the conductance
values of \emph{all} fundamental cuts of a given spanning tree. We integrate
the new edge rating into a leading multilevel graph partitioner and equip the
latter with a new greedy postprocessing for optimizing the maximum
communication volume (MCV). Experiments on bipartitioning frequently used
benchmark networks show that the postprocessing already reduces MCV by 11.3%.
Our new edge rating further reduces MCV by 10.3% compared to the previously
best rating with the postprocessing in place for both ratings. In total, with a
modest increase in running time, our new approach reduces the MCV of complex
network partitions by 20.4%
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