Mathematical Programming Computation

, Volume 2, Issue 2, pp 103–124 | Cite as

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

Full Length Paper


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.


Nonlinear combinatorial optimization Matroid optimization High-performance computing High-precision linear algebra 

Mathematics Subject Classification (2000)

90-08 90C27 90C26 


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Copyright information

© Springer and Mathematical Programming Society 2010

Authors and Affiliations

  1. 1.IBM T.J. Watson Research CenterYorktown HeightsUSA
  2. 2.Department of Computational and Applied MathematicsRice UniversityHoustonUSA

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