Optimum broadcasting and personalized communication in hypercubes

Four different communication problems are addressed in Boolean n-cube configured multiprocessors: (1) one-to-all broadcasting: distribution of common data from a single source to all other nodes; (2) one-to-all personalized communication: a single node sending unique data to all other nodes; (3) all-to-all broadcasting: distribution of common data from each node to all other nodes; and (4) all-to-all personalized communication: each node sending a unique piece of information to every other node. Three communication graphs (spanning trees) for the Boolean n-cube are proposed for the routing, and scheduling disciplines provably optimum within a small constant factor are proposed. With appropriate scheduling and concurrent communication on all ports of every processor, routings based on these two communication graphs offer a speedup of up to n/2, and O( square root n) over the routings based on the spanning binomial tree for cases (2)-(4) respectively. All three spanning trees offer optimal communication times for cases (2)-(4) and concurrent communication on all ports of every processor. Timing models and complexity analysis are verified by experiments on a Boolean-cube-configured multiprocessor.<>