1. A method, in a data processing system, for performing collective operations, the data processing system comprising a plurality of supernodes, the plurality of supernodes comprising a plurality of processor books, and the plurality of processor books comprising a plurality of processors, the method comprising: determining, in hardware of a parent processor in a first processor book of the data processing system, a number of other processors in a same or different processor book of the data processing system needed to execute the collective operation, thereby establishing a subset of processors comprising the parent processor and the other processors, wherein each processor in the plurality of processors comprises a first set of buses, a second set of buses, and a third set of buses, wherein each bus in the first set of buses couples the processor to each individual other processor in its respective processor book, wherein each bus in the second set of buses couples the processor to at least two processor books within its respective supernode, and wherein each bus in the third set of buses couples the processor to at least four other supernodes within the data processing system; logically arranging, in hardware of the parent processor, the subset of processors as a plurality of nodes in a hierarchical structure; transmitting the collective operation to the subset of processors based on the hierarchical structure via at least one of the first set of buses, the second set of buses, and the third set of buses; receiving, in hardware of the parent processor, results from the execution of the collective operation from the other processors via at least one of the first set of buses, the second set of buses, and the third set of buses; generating, in hardware of the parent processor, a final result of the collective operation based on the results received from execution of the collective operation by the other processors; and outputting the final result.