Abstract

Broadcasting is an information dissemination problem in a connected network, in which one node, called the originator, disseminates a message to all other nodes by placing a series of calls along the communication lines of the network. Once informed, the nodes aid the originator in distributing the message. Finding the broadcast time of a vertex in an arbitrary graph is NP-complete. The problem is solved polynomially only for a few classes of graphs. In this thesis, we study the broadcast problem in a class of graph called a Cactus Graph. A cactus graph is a connected graph in which any two simple cycles have at most one vertex in common. Equivalently, it is a connected graph in which every edge belongs to at most one simple cycle. We review broadcasting on subclasses of cactus graphs such as, the unicyclic graphs, necklace graphs, k-cycle graphs, 2-restricted cactus graphs and k-restricted cactus graphs. We then provide four heuristic algorithms that solves broadcasting on a k-cycle graph. A k-cycle graph is a collection of k cycles of arbitrary lengths all connected to a central vertex. Finally, we run simulations of these heuristic algorithms on different sized k-cycle graphs to compare and discuss the results.