219 research outputs found
Practical Minimum Cut Algorithms
The minimum cut problem for an undirected edge-weighted graph asks us to
divide its set of nodes into two blocks while minimizing the weight sum of the
cut edges. Here, we introduce a linear-time algorithm to compute near-minimum
cuts. Our algorithm is based on cluster contraction using label propagation and
Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both
sequential and shared-memory parallel implementations of our algorithm.
Extensive experiments on both real-world and generated instances show that our
algorithm finds the optimal cut on nearly all instances significantly faster
than other state-of-the-art algorithms while our error rate is lower than that
of other heuristic algorithms. In addition, our parallel algorithm shows good
scalability
Algorithms for Mapping Parallel Processes onto Grid and Torus Architectures
Static mapping is the assignment of parallel processes to the processing
elements (PEs) of a parallel system, where the assignment does not change
during the application's lifetime. In our scenario we model an application's
computations and their dependencies by an application graph. This graph is
first partitioned into (nearly) equally sized blocks. These blocks need to
communicate at block boundaries. To assign the processes to PEs, our goal is to
compute a communication-efficient bijective mapping between the blocks and the
PEs.
This approach of partitioning followed by bijective mapping has many degrees
of freedom. Thus, users and developers of parallel applications need to know
more about which choices work for which application graphs and which parallel
architectures. To this end, we not only develop new mapping algorithms (derived
from known greedy methods). We also perform extensive experiments involving
different classes of application graphs (meshes and complex networks),
architectures of parallel computers (grids and tori), as well as different
partitioners and mapping algorithms. Surprisingly, the quality of the
partitions, unless very poor, has little influence on the quality of the
mapping.
More importantly, one of our new mapping algorithms always yields the best
results in terms of the quality measure maximum congestion when the application
graphs are complex networks. In case of meshes as application graphs, this
mapping algorithm always leads in terms of maximum congestion AND maximum
dilation, another common quality measure.Comment: Accepted at PDP-201
ILP-based Local Search for Graph Partitioning
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that solve the partitioning problem to optimality. However, since those programs typically do not scale to large inputs, we adapt them to heuristically improve a given partition. We do so by defining a much smaller model that allows us to use symmetry breaking and other techniques that make the approach scalable. For example, in Walshaw\u27s well-known benchmark tables we are able to improve roughly half of all entries when the number of blocks is high
Cavity-enhanced Raman Microscopy of Individual Carbon Nanotubes
Raman spectroscopy reveals chemically specific information and provides
label-free insight into the molecular world. However, the signals are
intrinsically weak and call for enhancement techniques. Here, we demonstrate
Purcell enhancement of Raman scattering in a tunable high-finesse microcavity,
and utilize it for molecular diagnostics by combined Raman and absorption
imaging. Studying individual single-wall carbon nanotubes, we identify crucial
structural parameters such as nanotube radius, electronic structure and
extinction cross-section. We observe a 320-times enhanced Raman scattering
spectral density and an effective Purcell factor of 6.2, together with a
collection efficiency of 60%. Potential for significantly higher enhancement,
quantitative signals, inherent spectral filtering and absence of intrinsic
background in cavity-vacuum stimulated Raman scattering render the technique a
promising tool for molecular imaging. Furthermore, cavity-enhanced Raman
transitions involving localized excitons could potentially be used for gaining
quantum control over nanomechanical motion and open a route for molecular
cavity optomechanics
Finding All Global Minimum Cuts in Practice
We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum cuts using an optimized version of the algorithm of Nagamochi, Nakao and Ibaraki. In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes. We also give a new linear time algorithm to find the most balanced minimum cuts given as input the representation of all minimum cuts
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