Distributed Gröbner Bases Computation with MPJ

Groebner bases, an important building block in computer algebra, are computed on distributed memory parallel computers with multi-CPU compute nodes with increasing success. Based on previous efforts we present and compare new programs using the MPI message passing standard implemented using MPJ. MPJ is a specification of MPI for Java with efficient implementations. Also the new versions use one control communication channel between the master node and the worker nodes. In the hybrid version the polynomials are shared between the threads on a node and in the pure distributed version the polynomials are replicated on every process. 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 fields. We present first promising performance measurements.