Optimal Broadcasting in Fully Connected Trees

Broadcasting is disseminating information in a network where a specific message must spread to all network vertices as quickly as possible. Finding the minimum broadcast time of a vertex in an arbitrary network is proven to be NP-complete. However, this problem is solvable for a few families of networks. In this paper, we present an optimal algorithm for finding the broadcast time of any vertex in a fully connected tree ([Formula: see text]) in [Formula: see text] time. An [Formula: see text] is formed by attaching arbitrary trees to vertices of a complete graph of size [Formula: see text] where [Formula: see text] is the total number of vertices in the graph.