A modified parallel F4 algorithm for shared and distributed memory architectures

11 pages•Published: June 19, 2013

Abstract

In applications of symbolic computation an often required but complex procedure is the computation of Gröbner bases and hence it is obvious
to realize parallel algorithms to compute them. There are parallel flavours of the F4 algorithm using the special structure of the occurring matrices
to speed up the reduction. In this paper we start from this and present modifications allowing efficient computations of Gröbner bases on parallel architectures
using shared as well as distributed memory. To achieve this we concentrate on one objective: reducing the memory consumption and avoiding communication overhead.
We remove unrequired steps of the reduction, split the columns of the matrix in blocks for distribution and review the effectiveness of the SIMPLIFY function.
Finally we provide benchmarks with up to 256 distributed threads of an implementation which will be available at https://github.com/svrnm/parallelGBC.

Keyphrases: distributed memory architecture, f4 algorithm, gröbner basis, mpi

In: Laura Kovacs and Temur Kutsia (editors). SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science, vol 15, pages 70-80.

Links:	https://easychair.org/publications/paper/wS5z
	https://doi.org/10.29007/98fh

BibTeX entry

@inproceedings{SCSS2013:modified_parallel_F4_algorithm,
  author    = {Severin Neumann},
  title     = {A modified parallel F4 algorithm for shared and distributed memory architectures},
  booktitle = {SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science},
  editor    = {Laura Kovacs and Temur Kutsia},
  series    = {EPiC Series in Computing},
  volume    = {15},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/wS5z},
  doi       = {10.29007/98fh},
  pages     = {70-80},
  year      = {2013}}

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