1. An apparatus for 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 apparatus comprising a computer processor and a computer memory operatively coupled to the computer processor, the computer memory having disposed within it computer program instructions that, when executed by the computer processor, cause the apparatus to carry out the steps of: performing, by the plurality of child compute nodes, a first collective operation; receiving from each child compute node of the plurality of child compute nodes, by the first compute node, a result of the first collective operation performed by said each child compute node; for each result received from the plurality of child compute nodes, storing, by the first compute node, a timestamp indicating a time that said each child compute node completed the first collective operation, wherein storing the timestamp indicating the time that said each child compute node completed the first collection operation comprises: storing an entrance time that said each child compute node enters the first collective operation; and storing an exit time that said each child compute node exits the first collective operation; managing based on the stored timestamps, by the first compute node, execution of a second collective operation over the tree data communications network, including: identifying an order in which the plurality of child compute nodes completed the first collective operation including identifying a second set of child compute nodes of the plurality of child compute nodes that completed the first collective operation after a first set of child compute nodes of the plurality of child compute nodes, wherein identifying includes comparing the stored timestamps of the plurality of child compute nodes and, based on the comparison, assigning the plurality of child compute nodes into the first set or the second set including assigning at least two nodes of the plurality of child compute nodes into the first set and assigning at least two nodes of the plurality of child compute nodes into the second set; and based on the identified order of completion of the first collective operation, allocating additional resources to the second set of child compute nodes of the plurality of child compute nodes identified as completing the first collective operation after the first set of child compute nodes of the plurality of child compute nodes.