Parallel computation of gröbner bases on distributed memory machines

Hiroyuki Sawada, Satoshi Terasaki, Akira Aiba

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


This 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.

Original languageEnglish
Pages (from-to)207-222
Number of pages16
JournalJournal of Symbolic Computation
Issue number3
Publication statusPublished - 1994 Sept
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics


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