160 research outputs found
Convergence Speed of the Consensus Algorithm with Interference and Sparse Long-Range Connectivity
We analyze the effect of interference on the convergence rate of average
consensus algorithms, which iteratively compute the measurement average by
message passing among nodes. It is usually assumed that these algorithms
converge faster with a greater exchange of information (i.e., by increased
network connectivity) in every iteration. However, when interference is taken
into account, it is no longer clear if the rate of convergence increases with
network connectivity. We study this problem for randomly-placed
consensus-seeking nodes connected through an interference-limited network. We
investigate the following questions: (a) How does the rate of convergence vary
with increasing communication range of each node? and (b) How does this result
change when each node is allowed to communicate with a few selected far-off
nodes? When nodes schedule their transmissions to avoid interference, we show
that the convergence speed scales with , where is the
communication range and is the number of dimensions. This scaling is the
result of two competing effects when increasing : Increased schedule length
for interference-free transmission vs. the speed gain due to improved
connectivity. Hence, although one-dimensional networks can converge faster from
a greater communication range despite increased interference, the two effects
exactly offset one another in two-dimensions. In higher dimensions, increasing
the communication range can actually degrade the rate of convergence. Our
results thus underline the importance of factoring in the effect of
interference in the design of distributed estimation algorithms.Comment: 27 pages, 4 figure
SFC-based Communication Metadata Encoding for Adaptive Mesh
This volume of the series âAdvances in Parallel Computingâ contains the proceedings of the International Conference on Parallel Programming â ParCo 2013 â held from 10 to 13 September 2013 in Garching, Germany. The conference was hosted by the Technische UniversitĂ€t MĂŒnchen (Department of Informatics) and the Leibniz Supercomputing Centre.The present paper studies two adaptive mesh refinement (AMR) codes
whose grids rely on recursive subdivison in combination with space-filling curves
(SFCs). A non-overlapping domain decomposition based upon these SFCs yields
several well-known advantageous properties with respect to communication demands,
balancing, and partition connectivity. However, the administration of the
meta data, i.e. to track which partitions exchange data in which cardinality, is nontrivial
due to the SFCâs fractal meandering and the dynamic adaptivity. We introduce
an analysed tree grammar for the meta data that restricts it without loss of
information hierarchically along the subdivision tree and applies run length encoding.
Hence, its meta data memory footprint is very small, and it can be computed
and maintained on-the-fly even for permanently changing grids. It facilitates a forkjoin
pattern for shared data parallelism. And it facilitates replicated data parallelism
tackling latency and bandwidth constraints respectively due to communication in
the background and reduces memory requirements by avoiding adjacency information
stored per element. We demonstrate this at hands of shared and distributed
parallelized domain decompositions.This work was supported by the German Research Foundation (DFG) as part of the
Transregional Collaborative Research Centre âInvasive Computing (SFB/TR 89). It is
partially based on work supported by Award No. UK-c0020, made by the King Abdullah
University of Science and Technology (KAUST)
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