Methods, apparatuses, and computer program products for endpoint-based parallel data processing with non-blocking collective instructions in a parallel active messaging interface (‘PAMI’) of a parallel computer are provided. Embodiments include establishing by a parallel application a data communications geometry, the geometry specifying a set of endpoints that are used in collective operations of the PAMI, including associating with the geometry a list of collective algorithms valid for use with the endpoints of the geometry. Embodiments also include registering in each endpoint in the geometry a dispatch callback function for a collective operation and executing without blocking, through a single one of the endpoints in the geometry, an instruction for the collective operation.