Optimal Broadcasting in Fully Connected Trees

Abstract

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.

HUB-GA: A heuristic for universal lists broadcasting using genetic algorithm

“…Other researches include grid and tori [26], cube connected cycle [27], and shuffle exchange [28]. Later on, more algorithms for non-trivial topologies such as unicyclic graphs [29], fully connected trees [30], and tree of cycles [31] were developed, to name a few.…”

“…The reason for defining this function is quite obvious. In recent years, finding the broadcast time of a particular family of graphs has been an ongoing research question [20], [30], [39], [40], particularly under the universal list model [10], [45]- [48]. We claim that using the proposed algorithm, we can tackle this problem in two different ways: Firstly, our algorithm generates the actual broadcast scheme that minimizes its fitness function.…”