Methods, apparatus, and products are disclosed for performing an allreduce operation using shared memory that include: receiving, by at least one of a plurality of processing cores on a compute node, an instruction to perform an allreduce operation; establishing, by the core that received the instruction, a job status object for specifying a plurality of shared memory allreduce work units, the plurality of shared memory allreduce work units together performing the allreduce operation on the compute node; determining, by an available core on the compute node, a next shared memory allreduce work unit in the job status object; and performing, by that available core on the compute node, that next shared memory allreduce work unit.