Broadcasting in weighted-vertex graphs

In this thesis, we present a new model for information dissemination in communication networks. The model is defined on networks in which nodes are assigned some weights representing the internal delay they should pass before sending data to their neighbors. The new model, called weighted-vertex model, comes to have real world applications in parallel computation and satellite terrestrial networks. Broadcasting in weighted-vertex model is a generalized version of classical broadcasting problem, which is NP_Complete. The problem remains NP_Complete in some classes of weighed-vertex graphs. We show existence of approximation algorithms for the broadcasting problem in weighted vertex model, as well as better approximations for specific subclasses of weighted graphs. In addition we study broadcasting in complete weighted graphs and present an algorithm for finding the optimum solution in this case. Broadcasting in complete graphs with uniform weights is studied separately. Finally we introduce some heuristics for the problem and compare their performance using computer simulations

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