  We discuss several combinatorial problems that arise when one looks at
computational algorithms for highly symmetric networks of processors. More
specifically, we are interested in minimal times associated with four
communication tasks (defined more precisely below): universal broadcast, every
processor has a vector that it wishes to broadcast to all the others; universal
accumulation, every processor wishes to receive the sum of all the vectors
being sent to it by all the other processors; universal exchange, every
processor wishes to exchange a vector with each other processor; and global
summation, every processor wants the sum of the vectors in all the processors
