Broadcasting in Harary Graphs

With the increasing popularity of interconnection networks, efficient information dissemination has become a popular research area. Broadcasting is one of the information dissemination primitives. Broadcasting in a graph is the process of transmitting a message from one vertex, the originator, to all other vertices of the graph. We follow the classical model for broadcasting. This thesis studies the Harary graph in depth. First, we find the diameter of Harary graph. We present an additive approximation algorithm for the broadcast problem in Harary graph. We also provide some properties for the graph like vertex transitivity, circulant graph and regularity. In the next part we introduce modified harary graph. We calculate the diameter and broadcast time for the graph. We will also provide 1-additive approximation algorithm to find the broadcast time in the modified harary graph

Time-Varying Graphs and Dynamic Networks

The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts are components of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for time-varying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Based on this definitional work, employing both existing results and original observations, we present a hierarchical classification of TVGs; each class corresponds to a significant property examined in the distributed computing literature. We then examine how TVGs can be used to study the evolution of network properties, and propose different techniques, depending on whether the indicators for these properties are a-temporal (as in the majority of existing studies) or temporal. Finally, we briefly discuss the introduction of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be published in Internation Journal of Parallel, Emergent and Distributed System