High-performance computer algebra: a Hecke algebra case study

Maier, P., Livesey, D., Loidl, H.-W. and Trinder, P. (2014) High-performance computer algebra: a Hecke algebra case study. In: Euro-Par 2014 Parallel Processing - 20th International Conference, Porto, Portugal, 25-29 Aug 2014, pp. 415-426. (doi:10.1007/978-3-319-09873-9_35)

Maier, P., Livesey, D., Loidl, H.-W. and Trinder, P. (2014) High-performance computer algebra: a Hecke algebra case study. In: Euro-Par 2014 Parallel Processing - 20th International Conference, Porto, Portugal, 25-29 Aug 2014, pp. 415-426. (doi:10.1007/978-3-319-09873-9_35)

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Publisher's URL: http://dx.doi.org/10.1007/978-3-319-09873-9_35

Abstract

We describe the first ever parallelisation of an algebraic computation at modern HPC scale. Our case study poses challenges typical of the domain: it is a multi-phase application with dynamic task creation and irregular parallelism over complex control and data structures.<p></p> Our starting point is a sequential algorithm for finding invariant bilinear forms in the representation theory of Hecke algebras, implemented in the GAP computational group theory system. After optimising the sequential code we develop a parallel algorithm that exploits the new skeleton-based SGP2 framework to parallelise the three most computationally-intensive phases. To this end we develop a new domain-specific skeleton, parBufferTryReduce. We report good parallel performance both on a commodity cluster and on a national HPC, delivering speedups up to 548 over the optimised sequential implementation on 1024 cores.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Trinder, Professor Phil and Maier, Dr Patrick
Authors: Maier, P., Livesey, D., Loidl, H.-W., and Trinder, P.
College/School:College of Science and Engineering > School of Computing Science

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