Time-relaxed broadcasting in communication networks

AbstractBroadcasting is the process of information dissemination in communication networks (modelled as graphs) whereby a message originating at one vertex becomes known to all members under the constraint that each call requires one unit of time and at every step any member can call at most one of its neighbours. A broadcast graph on n vertices is a network in which message can be broadcast in the minimum possible (=⌊log2n⌋) time regardless of the originator. Broadcast graphs having the smallest number of edges are called minimum broadcast graphs, and are subjects of intensive study. On the other hand, in Shastri (1995) we have considered how quickly broadcasting can be done in trees. In this paper, we study how the number of edges in a minimum broadcast graphs decrease, as we allow addition time over ⌊log2 n⌋, until we get a tree. In particular, the sparsest possible time-relaxed broadcast graphs are constructed for small n(⩽15) and very sparse time-relaxed broadcast graphs are given for larger n(⩽65). General constructions are also provided putting bounds which hold for all n. Some of these constructions make use of the techniques developed in Bermond et al. (1995, 1992) and Chau and Liestman (1985)

Broadcasting in DMA-bound bounded degree graphs

AbstractBroadcasting is an information dissemination process in which a message is to be sent from a single originator to all members of a network by placing calls over the communication lines of the network. In [2], Bermond, Hell, Liestman and Peters studied the effect, on broadcasting capabilities, of placing an upper bound on the graph's degree. In this paper, we generalize their results allowing calls to involve more than two participants. We give lower bounds and construct bounded degree graphs which allow rapid broadcasting. Our constructions use the nation of compounding graphs in de Bruijin digraphs. We also obtain asymptotic upper and lower bounds for broadcast time, as the maximum degree increases

The complexity of broadcasting in bounded-degree networks

Broadcasting concerns the dissemination of a message originating at one node of a network to all other nodes. This task is accomplished by placing a series of calls over the communication lines of the network between neighboring nodes, where each call requires a unit of time and a call can involve only two nodes. We show that for bounded-degree networks determining the minimum broadcast time from an originating node remains NP-complete.Comment: 6 page

Studies of interconnection networks with applications in broadcasting

The exponential growth of interconnection networks transformed the communication primitives into an important area of research. One of these primitives is the one-to-all communication, i.e. broadcasting. Its presence in areas such as static and mobile networks, Internet messaging, supercomputing, multimedia, epidemic algorithms, replicated databases, rumors and virus spreading, to mention only a few, shows the relevance of this primitive. In this thesis we focus on the study of interconnection networks from the perspective of two main problems in broadcasting: the minimum broadcast time problem and the minimum broadcast graph problem. Both problems are discussed under the 1-port constant model, which assumes that each node of the network can communicate with only one other node at a time and the transmitting time is constant, regardless of the size of the message. In the first part we introduce the minimum broadcast time function and we present two new properties of this function. One of the properties yields an iterative heuristic for the minimum broadcast time problem, which is the first iterative approach in approximating the broadcast time of an arbitrary graph. In the second part we give exact upper and lower bounds for the number of broadcast schemes in graphs. We also propose an algorithm for enumerating all the broadcast schemes and a random algorithm for broadcasting. In the third part we present a study of the spectra of Knödel graph and their applications. This study is motivated by the fact that, among the three known infinite families of minimum broadcast graphs, namely the hypercube, the recursive circulant, and the Knödel graph, the last one has the smallest diameter. In the last part we introduce a new measure for the fault tolerance of an interconnection network, which we name the global fault tolerance. Based on this measure, we make a comparative study for the above mentioned classes of minimum broadcast graphs, along with other classes of graphs with good communication properties

Improved upper bounds and lower bounds on broadcast function

Given a graph G=(V,E) and an originator vertex v, broadcasting is an information disseminating process of transmitting a message from vertex v to all vertices of graph G as quickly as possible. A graph G on n vertices is called broadcast graph if the broadcasting from any vertex in the graph can be accomplished in \lceil log n\rceil time. A broadcast graph with the minimum number of edges is called minimum broadcast graph. The number of edges in a minimum broadcast graph on n vertices is denoted by B(n). A long sequence of papers present different techniques to construct broadcast graphs and to obtain upper bounds on B(n). In this thesis, we study the compounding and the vertex addition broadcast graph constructions, which improve the upper bound on B(n). We also present the first nontrivial general lower bound on B(n)

Broadcasting in Harary Graphs

With the increasing popularity of interconnection networks, efficient information dissemination has become a popular research area. Broadcasting is one of the information dissemination primitives. Broadcasting in a graph is the process of transmitting a message from one vertex, the originator, to all other vertices of the graph. We follow the classical model for broadcasting. This thesis studies the Harary graph in depth. First, we find the diameter of Harary graph. We present an additive approximation algorithm for the broadcast problem in Harary graph. We also provide some properties for the graph like vertex transitivity, circulant graph and regularity. In the next part we introduce modified harary graph. We calculate the diameter and broadcast time for the graph. We will also provide 1-additive approximation algorithm to find the broadcast time in the modified harary graph

A general upper bound on broadcast function B(n) using Knodel graph

Broadcasting in a graph is the process of transmitting a message from one vertex, the originator, to all other vertices of the graph. We will consider the classical model in which an informed vertex can only inform one of its uninformed neighbours during each time unit. A broadcast graph on n vertices is a graph in which broadcasting can be completed in ceiling of log n to the base 2 time units from any originator. A minimum broadcast graph on n vertices is a broadcast graph that has the least possible number of edges, B(n), over all broadcast graphs on n vertices. This thesis enhances studies about broadcasting by applying a vertex deletion method to a specific graph topology, namely Knodel graph, in order to construct broadcast graphs on odd number of vertices. This construction provides an improved general upper bound on B(n) for all odd n except when n=2^k−1