Problems related to broadcasting in graphs

• Main Author: Grigoryan, Hayk
• Format: Others
• Published: 2013
• Online Access: http://spectrum.library.concordia.ca/977773/1/Grigoryan_PhD_F2013.pdf; Grigoryan, Hayk <http://spectrum.library.concordia.ca/view/creators/Grigoryan=3AHayk=3A=3A.html> (2013) Problems related to broadcasting in graphs. PhD thesis, Concordia University.

The data transmission delays become the bottleneck on modern high speed interconnection networks utilized by high performance computing or enterprise data centers. This motivates the study directed towards finding more efficient interconnection topologies as well as more efficient algorithms for information exchange between the nodes of the given network. Broadcasting is the process of distributing a message from a node, called the originator, to all other nodes of a communication network. Broadcasting is used as a basic communication primitive by many higher level network operations, which involve a set of nodes in distributed systems. Therefore, it is one the most important operations, which can determine the total efficiency of a given distributed system. We study interconnection networks via modeling them as graphs. The results described in this work can be used for efficient message routing algorithms in switch based interconnection networks as well as in the choice of the interconnection topologies of such networks. This thesis is divided into six chapters. Chapter 1 gives a general introduction to the research area and literature overview. Chapter 2 studies the family of graphs for which the broadcast time is equal to the diameter. Chapter 3 studies the routing and broadcasting problem in the Knodel graph. Chapter 4 studies the possible vertex degrees and the possible connections between vertices of different degrees in a broadcast graph. Using this, a new lower bound is obtained on broadcast function. Chapter 5 presents some miscellaneous results. Chapter 6 summarizes the thesis.