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In a multiprocessor network, sending a packet typically refers to start-up time and transmission time. To optimize these two times, as opposed to earlier solutions, a spanning tree and multiple spanning trees are constructed to solve four types of broadcasting problems in an (n, k)-star graph: one-to-all or all-to-all broadcasting with either one-port or all-port communication model, respectively. Since the proposed spanning tree has an optimal height, both one to-all and all-to-all broadcasting algorithms achieve nearly optimal start-up time and transmission time under all-port model and one-port model, and optimal transmission time under one-port model. By using multiple spanning trees, both one-to-all and all-to-all algorithms achieve nearly optimal transmission time under all-port model and one-port model.

Optimum Broadcasting Algorithms in (n, k)-Star Graphs Using Spanning Trees