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A New Construction of Broadcast Graphs

机译:广播图的新构造

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Given a graph G = (V, E) and an originator vertex v, broadcasting is an information disseminating process of transmitting a message from vertex v to all vertices of graph G as quickly as possible. A graph G on n vertices is called broadcast graph if the broadcasting from any vertex in the graph can be accomplished in [log n] time. A broadcast graph with the minimum number of edges is called minimum broadcast graphs. The number of edges in a minimum broadcast graph on n vertices is denoted by B(n). A long sequence of papers present different techniques to construct broadcast graphs and to obtain upper bounds on B(n). In this paper, we follow the compounding method to construct new broadcast graphs and improve the known upper bounds on B(n) for many values of n.
机译:给定一个图G =(V,E)和一个原始顶点v,广播是一种信息传播过程,该过程是将消息从顶点v尽可能快地传输到图G的所有顶点。如果可以在[log n]时间内完成图中任意顶点的广播,则n个顶点上的图形G称为广播图。具有最小数量的边的广播图称为最小广播图。 B(n)表示n个顶点上的最小广播图中的边数。一长串论文提出了构建广播图和获得B(n)上限的不同技术。在本文中,我们遵循复合方法来构造新的广播图,并针对许多n值提高B(n)的已知上限。

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