Broadcasting multiple messages in hypercubes

We investigate T/sub m/(Q/sub d/), the time required to broadcast m/spl ges/1 messages in a d-dimensional hypercube under the telephone model. We give exact values for T/sub m/(Q/sub d/) for m/spl les/2/sup d-1/ and for m/spl ges/2/sup d/+1. For 2/sup d-1/+1/spl les/m/spl les/2/sup d/, we produce an upper bound which is 1 larger than the lower bound. One consequence of our results is to disprove a lower bound due to Farley (1980).