Parallel and distributed Gröbner bases computation in JAS

Details Parallel and distributed Gröbner bases computation in JAS Parallel and distributed Gröbner bases computation in JAS

2010-07-30

arxiv.org/abs/1008.0011v1

Computer Science

Distributed, Parallel, and Cluster Computing

14 pages, 8 tables, 13 figures

Scientific paper

This paper considers parallel Gr\"obner bases algorithms on distributed memory parallel computers with multi-core compute nodes. We summarize three different Gr\"obner bases implementations: shared memory parallel, pure distributed memory parallel and distributed memory combined with shared memory parallelism. The last algorithm, called distributed hybrid, uses only one control communication channel between the master node and the worker nodes and keeps polynomials in shared memory on a node. The polynomials are transported asynchronous to the control-flow of the algorithm in a separate distributed data structure. The implementation is generic and works for all implemented (exact) fields. We present new performance measurements and discuss the performance of the algorithms.

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