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2013.52: Performance Analysis of Asynchronous Parallel Jacobi

2013.52: James Hook and Nick Dingle (2013) Performance Analysis of Asynchronous Parallel Jacobi.

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Abstract

The directed acyclic graph (DAG) associated with a parallel al- gorithm captures the order in which separate local computations are completed and how their outputs are subsequently used in further com- putations. Unlike in a synchronous parallel algorithm the DAG asso- ciated with an asynchronous parallel algorithm is not predetermined. Instead it is a product of the asynchronous timing dynamics of the machine and, as such, it is best thought of as a pseudorandom vari- able. In this paper we present a new tighter bound on the rate of convergence of asynchronous parallel Jacobi (APJ), which is based on statistical properties of the DAG and is valid for systems which satisfy a standard sufficient condition for convergence. We also describe an experiment in which we make a precise log of the calculations taking place during an implementation of APJ on a distributed memory multicore machine, which enables us to reconstruct and study the DAG. We demonstrate that our bound provides a good approximation of the true rate of convergence in these examples and show how problems in the algorithm’s implementation can affect the asynchronous timing dynamics and in turn the rate of convergence of the algorithm.

Item Type:MIMS Preprint
Uncontrolled Keywords:Asynchronous parallel Jacobi, chaotic iterations, parallel algorithm performance
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 60 Probability theory and stochastic processes
MSC 2000 > 65 Numerical analysis
MSC 2000 > 68 Computer science
MIMS number:2013.52
Deposited By:Mr James Hook
Deposited On:29 October 2013

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