Distributed Hybrid Gröbner Bases Computation

This paper considers parallel Grobner bases algorithms on distributed memory parallel computers with multi-core compute nodes. We improve the pure distributed algorithm by an hybrid approach where on the compute nodes parallel threads for each available processor can be used. With this algorithm only one communication channel between the master node and the worker nodes is needed. By this we also improve memory footprint by sharing the polynomials in memory between the threads on a node. The communication is slightly more complicated and requires tagged messages to differentiate between request and result messages sent by multiple threads. Java object serialization is improved by using marshalled objects to reduce serialization overhead in the distributed list communication.