Efficient high-precision matrix algebra on parallel architectures for nonlinear combinatorial optimization

Type
Article

Authors
Gunnels, John
Lee, Jon
Margulies, Susan

Online Publication Date
2010-06-19

Print Publication Date
2010-06

Date
2010-06-19

Abstract
We provide a first demonstration of the idea that matrix-based algorithms for nonlinear combinatorial optimization problems can be efficiently implemented. Such algorithms were mainly conceived by theoretical computer scientists for proving efficiency. We are able to demonstrate the practicality of our approach by developing an implementation on a massively parallel architecture, and exploiting scalable and efficient parallel implementations of algorithms for ultra high-precision linear algebra. Additionally, we have delineated and implemented the necessary algorithmic and coding changes required in order to address problems several orders of magnitude larger, dealing with the limits of scalability from memory footprint, computational efficiency, reliability, and interconnect perspectives. © Springer and Mathematical Programming Society 2010.

Citation
Gunnels J, Lee J, Margulies S (2010) Efficient high-precision matrix algebra on parallel architectures for nonlinear combinatorial optimization. Math Prog Comp 2: 103–124. Available: http://dx.doi.org/10.1007/s12532-010-0014-4.

Acknowledgements
We gratefully acknowledge the use of the IBM Shaheen (which at the time of ourexperiments was an 8-rack Blue Gene/P supercomputer housed at the IBM T.J. Watson Research Center).The IBM Shaheen is now owned and operated by the King Abdullah University of Science and Technology(KAUST). We would like to thank Bob Walkup at IBM Research for his help in many aspects of this work,including the use of his performance-counter library for performance evaluation and Fred Mintzer at IBMResearch for arranging for our use of the Blue Gene/P Supercomputer. We are deeply indebted to DavidBailey and his team for the ARPREC software package and documentation. Our work was partially car-ried out, while S. Margulies was a graduate student at U.C. Davis, under an Open Collaborative Researchagreement between IBM and U.C. Davis.

Publisher
Springer Nature

Journal
Mathematical Programming Computation

DOI
10.1007/s12532-010-0014-4

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