Space exploration using parallel orbits: a study in parallel symbolic computing

Vladimir Janjic, Christopher Mark Brown, Max Neunhoeffer, Kevin Hammond, Stephen Alexander Linton, Hans-Wolfgang Loidl

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


Orbit enumerations represent an important class of mathematical algorithms which is widely used in computational discrete mathematics. In this paper, we present a new shared-memory implementation of a generic Orbit skeleton in the GAP computer algebra system [5]. By defining a skeleton, we are easily able to capture a wide variety of concrete Orbit enumerations that can exploit the same underlying parallel implementation. We also propose a generic cost model for predicting the speedups that our Orbit skeleton will deliver for a given application on a given parallel system. We demonstrate the scalability of our implementation on a 64-core shared-memory machine. Our results show that we are able to obtain good speedups over sequential GAP programs (up to 25.27 on 64 cores).
Original languageEnglish
Title of host publicationParallel Computing
Subtitle of host publicationAccelerating Computational Science and Engineering (CSE)
Editors Michael Bader, Arndt Bode, Hans-Joachim Bungartz, Michael Gerndt, Gerhard R. Joubert, Frans Peters
PublisherIOS Press
Number of pages8
ISBN (Electronic)978-1-61499-381-0
ISBN (Print)978-1-61499-380-3
Publication statusPublished - Sept 2013

Publication series

NameAdvances in Parallel Computing
PublisherIOS Press
ISSN (Print)0927-5452
ISSN (Electronic)1879-808X


  • Symbolic computation
  • Orbit calculation
  • Skeleton
  • Parallelism


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