A parallel computer comprises a plurality of compute nodes organized into at least one operational group for collective parallel operations. Each compute node is assigned a unique rank and is coupled for data communications through a global combining network. One compute node is assigned to be a logical root. A send buffer and a receive buffer is configured. Each element of a contribution of the logical root in the send buffer is contributed. One or more zeros corresponding to a size of the element are injected. An allreduce operation with a bitwise OR using the element and the injected zeros is performed. And the result for the allreduce operation is determined and stored in each receive buffer.