Optimal Communication Algorithms for Hypercubes

We consider several basic communication problems in a hypercube network of processors. These include the problem of simultaneous broadcast of the same packet from every processor to all other pro-cessors and the problem of simultaneous exchange of different packets between every pair of processors. The algorithms proposed for these problems are optimal in terms of execution time and communication resource requirements, that is, they require the minimum possible number of time steps and packet transmissions. This is a particularly strong form of optimality, which has not been considered in earlier investigations