article no. PC981500 Complexity and Approximations for Multimessage Multicasting 1

We consider multimessage multicasting over the n processor complete (or fully connected) static network (MM C). First we present a linear time algorithm that constructs for every degree d problem instance a communication schedule with total communication time at most d 2, where d is the maximum number of messages that each processor may send or receive. Then we present degree d problem instances such that all their communication schedules have total communication time at least d 2. We observe that our lower bound applies when the fan-out (maximum number of processors receiving any given message) is huge, and thus the number of processors is also huge. Since this environment is not likely to arise in the near future, we turn our attention to the study of important subproblems that are likely to arise in practice. We show that when each message has fan-out k=1 the MMC problem corresponds to the makespan openshop preemptive scheduling problem which can be solved in polynomial time and show that for k 2 our problem is NP-complete and remains NP-complete even when forwarding is allowed