| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 89 === Given an interconnection network, if we represent the processors as vertices, and the communication links as edges, then we can construct a graph model for this network. For this graph G=(V, E), assume that there is a vertex v0, outside the graph G, which is called the sender. The vertex v0 has a message, which has to be transmitted to all the vertices of G. The transmission should carried out as follows: in each time unit, the sender can send the message to any vertex of G, and at the same time, the vertices in G that knows already the message, sends it to his neighbors. A transmitting scheme allowing to all vertices to receive the message in t time units and requiring the vertex v0 to send the message s times is called a (t, s)-transmitting scheme, where . We called t the transmitting time, and s, the workload of the host. We aimed to find an optimal transmitting scheme, i.e. a transmitting scheme such that t is minimized while s is also minimized. In this paper, we consider the (t, s)-transmitting costs of union of paths and cycles, and complete k-nary trees.
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