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Dimensional Broadcast Schemes and Their Applications in Broadcast Graphs

Title:

Dimensional Broadcast Schemes and Their Applications in Broadcast Graphs

Fakharan, Mohammadhossein ORCID: https://orcid.org/0009-0008-8366-4051 (2025) Dimensional Broadcast Schemes and Their Applications in Broadcast Graphs. PhD thesis, Concordia University.

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Abstract

In a graph G = (V,E), where V and E are the sets of vertices and edges of G, respectively, broadcasting is an information dissemination process of distributing a message from one vertex, which is called the originator, to all other vertices of the graph. Spreading information is one of the
important tasks of a modern interconnection network. This process is called broadcasting. A huge amount of research was conducted in this area.
In this thesis, we will mainly focus on structural and algorithmic aspects of broadcasting in special families of graphs, particularly hypercubes and Knodel graphs. We investigate hypercubes as canonical examples of minimum broadcast graphs, where we develop an algorithm to generate and enumerate all minimum-time broadcast schemes. Our analysis confirms that every such scheme on a hypercube is also a minimum-distance broadcast scheme. Subsequently, we shift our attention to Knodel graphs, exploring their potential as broadcast
graphs under both standard and reversed dimensional broadcast schemes with cyclic shifts and arbitrarily dimension repetitions. We determine all values of n for which these schemes are valid and
identify structural properties that maximize broadcast efficiency. A new general upper bound on the broadcast function B(n) for odd n (excluding n = 2^k−1) is then established using a vertex deletion approach. In this context, we also resolve an open question concerning the existence of minimum average time broadcast graphs.
Finally, we extend our investigations to generalized Knodel graphs, characterizing the values of n for which they admit certain valid dimensional broadcast schemes. Our results contribute new insights
toward understanding the relationship between graph structure and information dissemination efficiency.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering
Item Type:Thesis (PhD)
Authors:Fakharan, Mohammadhossein
Institution:Concordia University
Degree Name:Ph. D.
Program:Computer Science
Date:26 November 2025
Thesis Supervisor(s):Harutyunyan, Hovhannes
ID Code:996508
Deposited By: Mohammadhossein Fakharan
Deposited On:29 Jun 2026 15:32
Last Modified:29 Jun 2026 15:32

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