Broadcasting in grid graphs

This work consists of two separate parts. The first part deals with the problem of multiple message broadcasting, and the topic of the second part is line broadcasting. Broadcasting is a process in which one vertex in a graph knows one or more messages. The goal is to inform all remaining vertices as fast as possible. In this work we consider a special kind of graphs, grids.; In 1980 A. M. Farley showed that the minimum time required to broadcast a set of M messages in any connected graph with diameter d is d + 2(M − 1). This work presents an approach to broadcasting multiple messages from the corner vertex of a 2-dimensional grid. This approach gives us a broadcasting scheme that differs only by 2 (and in the case of an even x even grid by only 1) from the above lower bound.; Line broadcasting describes a different variant of the broadcasting process. A. M. Farley showed that line broadcasting can always be completed in [log n] time units in any connected graph on n vertices. He defined three different cost measures for line broadcasting. This work presents strategies for minimizing those costs for various grid sizes.