Improved Upper Bound on -Time-Relaxed -Broadcasting Communication Networks

Broadcasting is a process in which an individual has an item of information which needs to be transmitted to all of the members in a network (which is viewed as a connected graph). -broadcasting is a variant of broadcasting in which each processor can transmit the message to up to of its neighbors in one time unit. Another variant of broadcasting is the concept of m-time-relaxed broadcasting, where we allow adding time units to the optimal broadcast time, in exchange for fewer edges. The combination of -time-relaxed and broadcasting is studied in this paper. The result shown here is an improvement in the upper bound obtained by Harutyunyan and Listman in [9] that constructs a communication network model, namely, a connected graph, which admits the -time-relaxed -broadcasting. In addition, we generalize (for ) and prove a conjecture of Shastri [18] concerning the monotonicity of such -time-relaxed models with respect to (the number of vertices in this graph).