1. A method of performing a deterministic reduction operation in a parallel computer, the parallel computer comprising a plurality of compute nodes, each compute node comprising a plurality of computer processors and a CAU (Collectives Acceleration Unit), the CAU coupling computer processors of compute nodes to one another for data communications in a cluster data communications network, the method comprising: organizing a plurality of processors of the parallel computer and a CAU into a branched tree topology, wherein the CAU comprises a root of the branched tree topology and the processors comprise children of the root CAU; establishing a receive buffer comprising a plurality of receive elements, each receive element associated with one of the processors in the branched tree topology and configured to store the associated processor's contribution data; receiving, by the root CAU in any order from the processors in the branched tree topology, each processor's contribution data; tracking receipt of each processor's contribution data; and reducing, by the root CAU, only after receipt of contribution data from all processors in the branched tree topology, the contribution data stored in the receive buffer in a predefined order.