Heuristic Algorithms For Broadcasting In Cactus Graphs

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

Optimal broadcasting in treelike graphs

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 different classes of graphs which have various similarities to trees. The unicyclic graph is the simplest graph family after trees, it is a connected graph with only one cycle in it. We provide a linear time solution for the broadcast problem in unicyclic graphs. We also studied graphs with increasing number of cycles and complexity and provide again polynomial time solutions. These graph families are: tree of cycles, necklace graphs, and 2-restricted cactus graphs. We also define the fully connected tree graphs and provide a polynomial solution and use these results to obtain polynomial solution for the broadcast problem in tree of cliques and a constant approximation algorithm for the hierarchical tree cluster networks