1. An apparatus for runtime optimization of an application executing on a parallel computer, the parallel computer having a plurality of compute nodes organized into a communicator, 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: determining, by each compute node, whether a collective operation is root-based; if the collective operation is not root-based, establishing a tuning session administered by a self tuning module for the collective operation in dependence upon an identifier of a call site of the collective operation and executing the collective operation in the tuning session; if the collective operation is root-based, determining, through use of a single other collective operation, whether all compute nodes executing the application identified the collective operation at the same call site; if all compute nodes executing the application identified the collective operation at the same call site, establishing a tuning session administered by the self tuning module for the collective operation in dependence upon the identifier of the call site of the collective operation and executing the collective operation in the tuning session; and if all compute nodes executing the application did not identify the collective operation at the same call site, executing the collective operation without establishing a tuning session.