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Tight Bounds on Minimum Broadcast Networks
, 1991
"... A broadcast graph is an nvertex communication network that supports a broadcast from any one vertex to all other vertices in optimal time dlg ne, given that each message transmission takes one time unit and a vertex participates in at most one transmission per time step. This paper establishes t ..."
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Cited by 17 (0 self)
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A broadcast graph is an nvertex communication network that supports a broadcast from any one vertex to all other vertices in optimal time dlg ne, given that each message transmission takes one time unit and a vertex participates in at most one transmission per time step. This paper establishes tight bounds for B(n), the minimum number of edges of a broadcast graph, and D(n), the minimum maxdegree of a broadcast graph. Let L(n) denote the number of consecutive leading 1's in the binary representation of integer n \Gamma 1. We show B(n) = \Theta(L(n) \Delta n) and D(n) = \Theta(lg lg n+L(n)), and for every n we give a construction simultaneously within a constant factor of both lower bounds. For all n we also construct graphs with O(n) edges and O(lg lg n) maxdegree requiring at most dlg ne + 1 time units to broadcast. Our broadcast protocols may be implemented with local control and O(lg lg n) bits overhead per message.
FaultTolerant Minimum Broadcast Networks
 NETWORKS
, 1996
"... Broadcasting is the task of transmitting a message originated at one processor of a communication network to all other processors in the network. A minimal kfault tolerant broadcast network is a communication network on n vertices in which any processor can broadcast in spite of up to k line failu ..."
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Cited by 5 (1 self)
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Broadcasting is the task of transmitting a message originated at one processor of a communication network to all other processors in the network. A minimal kfault tolerant broadcast network is a communication network on n vertices in which any processor can broadcast in spite of up to k line failures in optimal time Tn (k). In this paper we study B k (n), the minimum number of communication lines of any minimal kfault tolerant broadcast network on n processors. We give the value of B k (n) for several values of n and k and, in case k ! blog nc, give almostminimum kfaulttolerant broadcast networks. Research partially done while visiting the Sonderforschungsbreich "Diskrete Strukturen in der Mathematik" of Bielefeld University. The work of this author was partially supported by the Italian Ministry of University and of Scientific Research in the framework of the "Algoritmi, Modelli di Calcolo e Strutture Informative" project. 1 Introduction This paper deals with graphs in w...
Communication Complexity of FaultTolerant Information Diffusion
 in: Proceedings of Fifth IEEE Symposium on Parallel and Distributed Processing
, 1993
"... This paper considers problems of faulttolerant information diffusion in a network with cost function. We show that the problem of determining the minimum cost necessary to perform fault tolerant gossiping among a given set of participants is NPhard and give approximate (with respect to the cost ..."
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This paper considers problems of faulttolerant information diffusion in a network with cost function. We show that the problem of determining the minimum cost necessary to perform fault tolerant gossiping among a given set of participants is NPhard and give approximate (with respect to the cost) faulttolerant gossiping algorithms. We also analyze the communication time and communication complexity of faulttolerant gossiping algorithms. Finally, we give an optimal cost fault tolerant broadcasting algorithm and apply our results to the atomic commitment problem. Key Words: Communication Networks, Gossiping, Atomic Commitment, FaultTolerance. Research partially supported by the Italian Ministry of University and of Scientific Research in the framework of the "Algoritmi, Modelli di Calcolo e Strutture Informative" project. 1 Introduction In this paper we study the problems of faulttolerant broadcasting, gossiping, and atomic commitment in a weighted network. Gossiping in ...
The Impact of Mobility on Broadcast Communication
"... Reliable broadcast is an important building block for the design and implementation of various Mobile Ad Hoc Network (MANET) protocols. In this paper, we study the impact of mobility on broadcast communication by slowly relaxing the constraints on mobility. As we move toward a less restrictive mobil ..."
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Reliable broadcast is an important building block for the design and implementation of various Mobile Ad Hoc Network (MANET) protocols. In this paper, we study the impact of mobility on broadcast communication by slowly relaxing the constraints on mobility. As we move toward a less restrictive mobility model, we need to pay more in term of communication overhead and latency. Hence, there is a tradeoff between having an efficient broadcast protocol and an unrestricted mobility pattern. While such a tradeoff should be intuitively apparent, the contribution of this paper is to clearly point out the limitations of current solution approaches and analyze how far we can relax mobility for broadcast protocols to work correctly. We also analyze a few broadcast protocols and show that these broadcast protocols that claim to work correctly for MANETs, assume that there is some limitation on node mobility. When exposed to a more relaxed mobility model, these protocols have mixed results. Hence, each broadcast protocol needs to be qualified with the mobility model it supports. 1