Strategy-Accurate Parallel Buchberger Algorithms

Strategy-Accurate Parallel Buchberger Algorithms

We describe two parallel versions of the Buchberger algorithm for computing Gröbner bases, one for the general case and one for homogeneous ideals, which exploit coarse grain parallelism. For the general case, to avoid the growth in number and complexity of the polynomials to reduce, the algorithm adheres strictly to the same strategies as the best sequential implementation. A suitable communic...

A Strategy-accurate Parallel Buchberger Algorithm

We describe a parallelized form of Buchberger algorithm that is strategy-accurate, i.e. that exactly simulates the sequential algorithm. The algorithm has been experimentally implemented on a a network of workstations, and notwithstanding some problems the experimentation gives evidence that the approach is viable. Plans for further work are discussed.

Parallel Buchberger Algorithms on Virtual Shared Memory KSR1

We develop parallel versions of Buchbergers Gröbner Basis algorithm for a virtual shared memory KSR1 computer. A coarse grain version does S-polynomial reduction concurrently and respects the same critical pair selection strategy as the sequential algorithm. A fine grain version parallelizes polynomial reduction in a pipeline and can be combined with the parallel S-polynomial reduction. The alg...

A parallel Buchberger algorithm for multigraded ideals

We demonstrate a method to parallelize the computation of a Gröbner basis for a homogenous ideal in a multigraded polynomial ring. Our method uses anti-chains in the lattice N to separate mutually independent S-polynomials for reduction.

Parallel Polynomial Operations in the Buchberger Algorithm