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TitleParallel computation of Gröbner bases on distributed memory machines
Author(s) Akira Aiba, Hiroyuki Sawada, Satoshi Terasaki
TypeArticle in Journal
AbstractThis paper reports our work on parallelizing an algorithm computing Gröbner bases on a distributed memory parallel machine. When computing Gröbner bases, the efficiency of computation is dominated by the total number of S-polynomials. To decrease the total number of S-polynomials it is necessary to apply a selection strategy that selects the minimum polynomial as a new element of an intermediate base.
On a distributed memory parallel machine, as opposed to a shared memory parallel machine, we have to take into account non-trivial communication costs between processors. To reduce such communication costs, it is better to employ coarse grained parallelism rather than fine grained parallelism.
We adopt a manager-worker model. S-polynomials are reduced in worker processes in parallel, and the minimum polynomial is selected in the manager process. To implement the selection strategy in this parallel model, synchronization between worker processes is required for every selection of a new element of the intermediate base. However, in spite of synchronization, introducing the selection strategy produces not only a better absolute computation speed but also better speedup with multi-processors. We achieved about 8 times speedup with 64 processors for large problems, T-6 and Ex-17.
URL dx.doi.org/10.1006/jsco.1994.1045
JournalJournal of Symbolic Computation
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Translation No
Refereed Yes