# Multi-Message Multicasting

## Abstract

We consider the Multi-Message Multicasting problem for the *n* processor fully connected static network. We present an efficient algorithm to construct a communication schedule with total communication time at most *d*^{2}, where *d* is the maximum number of messages a processor may send (receive). We present an algorithm to construct for any problem instance of degree *d* and fan-out *k* (maximum number of processors that may receive a given message) a communication schedule with total communication time at most *qd+k*^{1/q(d}−1), for any integer *q*≥2. The time complexity bound for our algorithm is *O(n(d(q*+*k*^{1/q}))^{q}). Our main result is a linear time approximation algorithm with a smaller approximation bound for small values of *k*(<100). We discuss applications and show how to adapt our algorithms to dynamic networks such as the Benes network, the interconnection network used in the Meiko CS-2.

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