1. A method of collective operation management in a parallel computer, the parallel computer including a first compute node operatively coupled for data communications over a tree data communications network with a plurality of child compute nodes, the method comprising: performing, by each child compute node, a first collective operation; for each child compute node: receiving from the child compute node, by the first compute node, a result of the first collective operation performed by the child compute node; for each result received from the child compute node, storing, by the first compute node, a timestamp indicating a time that the child compute node completed the first collective operation; and managing based on the stored timestamps, by the first compute node, execution of a second collective operation over the tree data communications network.