Efficient All-to-All Communication Patterns in Hypercube and Mesh Topologies

Some application programs on distributed memory parallel computers occasionally require an "all-to-all" communication pattern, where each compute node must send a distinct message to each other compute node. Assuming that each node can send and receive only one message at a t ime, the all-to-all pattern must be implemented as a sequence of phases in which certain nodes send and receive messages. r f there are p compute nodes, then at least p-1 phases are needed to complete the operation. A proof of a schedule achieving this lower bound on a circuit switched hypercube with fuced routing is given. This lower bound cannot be achieved on a 2 dimensional mesh. On an axa mesh, dl4 is shown to be a lower bound and a schedule with this number of phases is given. Whether hypercubes or meshes are better for this algorithm depends on the relative bandwidths of the communication channels.