Multi-broadcasting in Trees of a Given Diameter

The problem of Multi-broadcasting is defined as a process of relaying information in a network where a message originating at a vertex in the network is to be transmitted to the entire network by means of a series of calls placed over vertices in the network. This message transmission follows certain constraints, which are: each call requires one time unit and a node in the network can call not more than k of its adjacent vertices in one unit of time. Under k-broadcasting, we can see that in t time steps, at most (k+1)t members can be informed. Or, to inform the entire nertwork of n nodes, we require ⌈logk+1n⌉ time steps. In this paper, we study k-broadcasting in trees of a given diameter. We also study the minimum time required to multi-broadcast in a tree from any originator vertex. We present values for the maximum possible number of vertices in a tree of a given diameter (2 ≤ d ≤ 5) in which k-broadcasting takes place from any vertex in the tree.