Methods, parallel computers, and computer program products are disclosed for effecting a broadcast with an allreduce operation on a parallel computer, the parallel computer comprising a plurality of compute nodes, the compute nodes organized into at least one operational group of compute nodes for collective parallel operations of the parallel computer, each compute node in the operational group assigned a unique rank, the compute nodes of the operational group coupled for data communications through a global combining network; and one compute node assigned to be a logical root. Embodiments include configuring, by the logical root node, a send buffer having a contribution to be broadcast to each ranked node in the operational group; configuring, by all ranked nodes other than the logical root, a receive buffer for receiving the contribution from the logical root; and repeatedly for each element of the contribution of the logical root in the send buffer: contributing, by the logical root, the element of the contribution in the send buffer; injecting, by all ranked nodes other than the logical root, one or more zeros corresponding to a size of the element; performing, by all the compute nodes of the operational group, an allreduce operation with a bitwise OR using the element and the injected zeros, yielding a result for the allreduce operation; and storing in each receive buffer, by all ranked nodes other than the logical root, the result of the allreduce.