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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Eigenanalysis-based task mapping on parallel computers with cellular networks


Authors: Peng Zhang, Yuxiang Gao, Janet Fierson and Yuefan Deng
Journal: Math. Comp. 83 (2014), 1727-1756
MSC (2010): Primary 68M10, 90C06, 90C20, 90C35; Secondary 68M07, 90C90, 65B99, 15A63, 15A18
Published electronically: December 16, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: Through eigenanalysis of communication matrices, we develop a new objective function formulation for mapping tasks to parallel computers with cellular networks. This new formulation significantly speeds up the solution process through consideration of the symmetries in the supply matrix of a network and a transformation of the demand matrix of any application. The extent of the speedup is not easily obtainable through analytical means for most production networks. However, numerical experiments of mapping wave equations on 2D mesh onto 3D torus networks by simulated annealing demonstrate a far superior convergence rate and quicker escape from local minima with our new formulation than with the standard graph theory-based one.


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Additional Information

Peng Zhang
Affiliation: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794
Email: Peng.Zhang@stonybrook.edu

Yuxiang Gao
Affiliation: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794
Email: Yuxiang.Gao@stonybrook.edu

Janet Fierson
Affiliation: Department of Mathematics and Computer Science, La Salle University, Philadelphia, Pennsylvania 19141
Email: fierson@lasalle.edu

Yuefan Deng
Affiliation: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794
Email: Yuefan.Deng@stonybrook.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02770-6
PII: S 0025-5718(2013)02770-6
Keywords: Eigenanalysis, task mapping, large-scale optimization, quadratic programming, graph theory
Received by editor(s): October 18, 2010
Received by editor(s) in revised form: August 26, 2011, and November 17, 2012
Published electronically: December 16, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.