1. A method of executing a collective operation algorithm in a parallel computer, the parallel computer comprising a plurality of compute nodes, the compute nodes coupled for data communications by one or more data communications networks, the compute nodes organized in an operational group for collective operations, the method comprising: determining, by a compute node of an operational group, a required number of participants for execution of a collective operation algorithm; determining, by the compute node, a number of contributing nodes having data to participate in the algorithm; calculating, by the compute node, a number of ghost nodes to participate in the algorithm, wherein the number of ghost nodes being the required number of participants minus the number of contributing nodes having data to participate; selecting from a plurality of ghost nodes, by the compute node, the calculated number of ghost nodes for participation in the execution of the algorithm; and executing the algorithm with both the selected ghost nodes and the contributing nodes.