8 research outputs found
Multi-level algorithms for modularity clustering
Modularity is one of the most widely used quality measures for graph
clusterings. Maximizing modularity is NP-hard, and the runtime of exact
algorithms is prohibitive for large graphs. A simple and effective class of
heuristics coarsens the graph by iteratively merging clusters (starting from
singletons), and optionally refines the resulting clustering by iteratively
moving individual vertices between clusters. Several heuristics of this type
have been proposed in the literature, but little is known about their relative
performance.
This paper experimentally compares existing and new coarsening- and
refinement-based heuristics with respect to their effectiveness (achieved
modularity) and efficiency (runtime). Concerning coarsening, it turns out that
the most widely used criterion for merging clusters (modularity increase) is
outperformed by other simple criteria, and that a recent algorithm by Schuetz
and Caflisch is no improvement over simple greedy coarsening for these
criteria. Concerning refinement, a new multi-level algorithm is shown to
produce significantly better clusterings than conventional single-level
algorithms. A comparison with published benchmark results and algorithm
implementations shows that combinations of coarsening and multi-level
refinement are competitive with the best algorithms in the literature.Comment: 12 pages, 10 figures, see
http://www.informatik.tu-cottbus.de/~rrotta/ for downloading the graph
clustering softwar
Real-time dynamic hardware reconfiguration for processors with redundant functional units
The tiny logic elements in modern integrated circuits increase the rate of transient failures significantly. Therefore, redundancy on various levels is necessary to retain reliability. However, for mixed-criticality scenarios, the typical processor designs offer either too little fault-tolerance or too much redundancy for one part of the applications. Amongst others, we specifically address redundant processor internal functional units (FU) to cope with transient errors and support wear leveling. A real-time operating system (RTOS) was extended to control our prototypical hardware platform and, since it can be configured deterministically within few clock cycles, we are able to reconfigure the FUs dynamically, at process switching time, according to the specified critically of the running processes. Our mechanisms were integrated into the Plasma processor and the Plasma-RTOS. With few changes to the original software code, it was, for example, possible to quickly change from fault-detecting to fault-correcting modes of the processor on demand
Searching for network modules
When analyzing complex networks a key target is to uncover their modular
structure, which means searching for a family of modules, namely node subsets
spanning each a subnetwork more densely connected than the average. This work
proposes a novel type of objective function for graph clustering, in the form
of a multilinear polynomial whose coefficients are determined by network
topology. It may be thought of as a potential function, to be maximized, taking
its values on fuzzy clusterings or families of fuzzy subsets of nodes over
which every node distributes a unit membership. When suitably parametrized,
this potential is shown to attain its maximum when every node concentrates its
all unit membership on some module. The output thus is a partition, while the
original discrete optimization problem is turned into a continuous version
allowing to conceive alternative search strategies. The instance of the problem
being a pseudo-Boolean function assigning real-valued cluster scores to node
subsets, modularity maximization is employed to exemplify a so-called quadratic
form, in that the scores of singletons and pairs also fully determine the
scores of larger clusters, while the resulting multilinear polynomial potential
function has degree 2. After considering further quadratic instances, different
from modularity and obtained by interpreting network topology in alternative
manners, a greedy local-search strategy for the continuous framework is
analytically compared with an existing greedy agglomerative procedure for the
discrete case. Overlapping is finally discussed in terms of multiple runs, i.e.
several local searches with different initializations.Comment: 10 page
Load Balancing Strategies for Parallel . . .
Highly resolved numerical solutions of partial differential equations are important in many areas of science and technology. Only adaptive mesh refinement methods reduce the necessary work sufficiently, allowing the calculation of realistic problems. Block-structure