Methods, apparatus, and products are disclosed for executing an allgather operation on a parallel computer that includes a plurality of compute nodes organized into at least one operational group of compute nodes for collective parallel operations, each compute node in the operational group assigned a unique rank, that includes: determining a contention-free logical ring topology for the compute nodes in the operational group; configuring, for each compute node in the operational group according to the contention-free logical ring topology, a routing table to specify a forwarding path to the next compute node in the logical ring topology; and repeatedly, for each compute node in the operational group until each compute node has received contributions for all of the other compute nodes in the operational group, forwarding a contribution for the allgather operation to the next compute node in the logical ring topology along the forwarding path.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
 This invention was made with Government support under Contract No. B554331 awarded by the Department of Energy. The Government has certain rights in this invention.