1. Apparatus for performing collective reductions, broadcasts, and point-to-point message passing during parallel algorithm operations executing in a computing structure comprising a multitude of processing nodes, said apparatus comprising: a global collective network including routing devices interconnecting said nodes in a network configuration, said network configuration including a plurality of separate tree networks to perform global processing operations in the global collective network, said global processing operations including global broadcast operations, global reduction operations, and point-to-point message passing; each of the tree networks including a respective one, non-overlapping class of a multitude of said processing nodes; wherein said global collective network and routing device configuration provide low-latency communications in said computing structure.