10,181 research outputs found
Distributed Computation as Hierarchy
This paper presents a new distributed computational model of distributed
systems called the phase web that extends V. Pratt's orthocurrence relation
from 1986. The model uses mutual-exclusion to express sequence, and a new kind
of hierarchy to replace event sequences, posets, and pomsets. The model
explicitly connects computation to a discrete Clifford algebra that is in turn
extended into homology and co-homology, wherein the recursive nature of objects
and boundaries becomes apparent and itself subject to hierarchical recursion.
Topsy, a programming environment embodying the phase web, is available from
www.cs.auc.dk/topsy.Comment: 16 pages, 3 figure
Distributed computation of persistent homology
Persistent homology is a popular and powerful tool for capturing topological
features of data. Advances in algorithms for computing persistent homology have
reduced the computation time drastically -- as long as the algorithm does not
exhaust the available memory. Following up on a recently presented parallel
method for persistence computation on shared memory systems, we demonstrate
that a simple adaption of the standard reduction algorithm leads to a variant
for distributed systems. Our algorithmic design ensures that the data is
distributed over the nodes without redundancy; this permits the computation of
much larger instances than on a single machine. Moreover, we observe that the
parallelism at least compensates for the overhead caused by communication
between nodes, and often even speeds up the computation compared to sequential
and even parallel shared memory algorithms. In our experiments, we were able to
compute the persistent homology of filtrations with more than a billion (10^9)
elements within seconds on a cluster with 32 nodes using less than 10GB of
memory per node
Fast Distributed Computation of Distances in Networks
This paper presents a distributed algorithm to simultaneously compute the
diameter, radius and node eccentricity in all nodes of a synchronous network.
Such topological information may be useful as input to configure other
algorithms. Previous approaches have been modular, progressing in sequential
phases using building blocks such as BFS tree construction, thus incurring
longer executions than strictly required. We present an algorithm that, by
timely propagation of available estimations, achieves a faster convergence to
the correct values. We show local criteria for detecting convergence in each
node. The algorithm avoids the creation of BFS trees and simply manipulates
sets of node ids and hop counts. For the worst scenario of variable start
times, each node i with eccentricity ecc(i) can compute: the node eccentricity
in diam(G)+ecc(i)+2 rounds; the diameter in 2*diam(G)+ecc(i)+2 rounds; and the
radius in diam(G)+ecc(i)+2*radius(G) rounds.Comment: 12 page
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
On Distributed Computation in Noisy Random Planar Networks
We consider distributed computation of functions of distributed data in
random planar networks with noisy wireless links. We present a new algorithm
for computation of the maximum value which is order optimal in the number of
transmissions and computation time.We also adapt the histogram computation
algorithm of Ying et al to make the histogram computation time optimal.Comment: 5 pages, 2 figure
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