Exchanging messages of different sizes
Journal of Parallel and Distributed Computing
| Hi-index | 0.00 |
We consider Multimessage Multicasting over the $n$ processor complete (or fully connected) static network ($MM_{C}$) with Forwarding. We present an efficient algorithm that constructs for every degree $d$ problem instance a communication schedule with total communication time at most $2d$, where $d$ is the maximum number of messages that each processor may send (receive). Our algorithm consists of two phases. In the first phase a set of communications are scheduled to be carried out in $d$ time periods, and when these communications are performed the remaining problem becomes a multimessage unicasting problem of degree $d$. In the second phase we generate a communication schedule for this problem by reducing it to the Makespan Openshop Preemptive Scheduling problem which can be solved in polynomial time. The solution is the concatenation of the communication schedules for these two phases. Our centralized algorithms require all the communication information ahead of time. Applications where all of this information is readily available include iterative algorithms for solving linear equations, and most dynamic programming procedures. The Meiko CS-2 machine and in general computer systems with processors communicating via dynamic permutation networks whose basic switches can act as data replicators (e.g., $n$ by $n$ Benes network with 2 by 2 switches that can also act as data replicators) will also benefit from our results since the same schedules can be used for these systems.