In a parallel computer, performing a rooted-v collective operation by an operational group of compute nodes includes: identifying, in source code by a collective algorithm selection optimizing module, a gather operation followed by a rooted-v collective operation; replacing, by the collective algorithm selection optimizing module, the gather operation with an allgather operation; executing, by the compute nodes, the allgather operation; selecting, by each compute node in dependence upon results of the allgather operation, an algorithm for effecting the rooted-v collective operation; and executing, by each compute node, the rooted-v collective operation with the selected algorithm.