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)

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