Broadcasting in Weighted-Vertex Graphs

Abstract

In this paper a new model for information dissemination in communication network is presented. The model is defined on networks in which nodes are assigned some weights representing the internal delay they should pass before sending data to their neighbors. The new model, called weighted-vertex model, comes to have real world applications in parallel computation and satellite terrestrial networks. As a generalization of the classical model, optimum broadcasting in weighted-vertex model is NP Hard. The problem remains NP Hard in some classes of weighed-vertex graphs. We show existence of approximation algorithms for the broadcasting problem in weighted vertex model, as well as better approximations for specific subclasses of weighted graphs.The classical model of broadcasting models a network by an n-vertex graph G = (V, E). The communication in the network is assumed to be synchronous, i.e., occurs in discrete rounds, and in every round every processor is allowed to pick one of its neighbors, and send it a message. There has been plenty of research on the classical model during the last decades. To review some of the existing results, seeThe classical model of broadcasting does not always fit the requirements of real-world situations. This is the reason that several other models are presented each having its own properties (see for example [4], [5], [3]).Here we enhance the classical model to the graphs with weighted vertices resulting a new model called weightedvertex model. The weights assigned to the vertices may have different meanings. Each node may represent a smaller network such that the assigned weight be an upper bound for the broadcast time of that network. In a parallel machine, the weights assigned to processors can be interpreted as a kind of internal process each processor needs to perform before starting informing its neighbors (sometimes we regard the weights of the nodes as internal process or internal delay).The weights can also be considered as the delay for receiving the message due to input device limitations.Another application of weighted-vertex model is in SatelliteTerrestrial (ST) networks. These are networks in which a large number of nodes are interconnected by both satellite and terrestrial networks [1]. ST networks can effectively support multicast services. However the performance of these networks is not high when they are modeled by regular unweighted graphs. The reason is that the cost of satellite nodes is more than terrestrial nodes. To resolve this problem, ST networks has been modeled by weighted-vertex graphs in which the vertices representing satellite nodes have positive integer weights, while the vertices representing terrestrial nodes have 0 as their costs. The weight assigned to the satellite nodes is the sum of the costs of up-links and down-links connecting them to the terrestrial network. By including these vertices in the broadcast tree, their costs are included in the costs of trees [1], [13].While defining a new model, it may come to mind to put the weights on bot...