1. A method of constructing a logical tree topology in a parallel computer, the parallel computer comprising a plurality of compute nodes, each compute node comprising a hardware acceleration unit and executing an identical number of tasks, wherein the tasks of each node have a rank, the method comprising: creating a plurality of hardware acceleration groups, each hardware acceleration group comprising one task from each compute node, the one task from each compute node having the same rank; assigning one task of a root compute node as a global root of the logical tree topology; assigning tasks of the root compute node other than the global root as local children of the global root; assigning each of the global root and local children of the root compute node as a root of a subtree of tasks, wherein each subtree comprises the tasks of a hardware acceleration group; performing a broadcast operation in the logical tree topology including: transmitting broadcast data by the global root of the root compute node to the local children of the root compute node through shared memory; and transmitting the broadcast data in parallel by the global root and local children to tasks of the global root and local children's subtrees.