Methods and problems of communication in usual networks

Fraigniaud, Pierre; Lazard, Emmanuel

doi:10.1016/0166-218x(94)90180-5

Cited by 338 publications

(137 citation statements)

References 67 publications

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“…For more details, we refer the reader to [4]. Now let G be a finite group and K ≤ G. Assume that Γ = Cay(G, S) and Σ = Cos(G, K, S) for some generating set S of G. For a communication model M , let b M (Γ K ) be the minimum time required to complete broadcasting in the vertices of K from the identity element 1 (which is the message originator).…”

Section: Resultsmentioning

confidence: 99%

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Some Conclusions on Cayley Digraphs and Their Applications to Interconnection Networks

Xiao

Parhami

2004

Grid and Cooperative Computing

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Abstract.In this short communication, we survey the relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups and obtain some general results on homomorphism and broadcasting between them. We also obtain a factorization of Cayley digraphs on subgraphs. We discuss the applications of these results to well-known interconnection networks. These conclusions possess potential application to grid computing.

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Section: Resultsmentioning

confidence: 99%

“…Because H ≤ G ≤ Aut(Γ i ), the digraph Γ i is a Cayley digraph per [4]. In fact, it is easily proven that Γ i = Cay(H, S i ) and…”

Section: Proof Omittedmentioning

confidence: 99%

Some Conclusions on Cayley Digraphs and Their Applications to Interconnection Networks

Xiao

Parhami

2004

Grid and Cooperative Computing

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“…The goal is not to minimize the number of rounds, but the total cost of the broadcast trees. In [11] they also define a problem called scattering which involves one node broadcasting distinct messages to all the other nodes (very much like our single source multicast, where the multicast groups all have size one and are disjoint).…”

Section: Related Workmentioning

confidence: 99%

On generalized gossiping and broadcasting

Khuller¹,

Kim²,

Wan³

2006

Journal of Algorithms

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Abstract. The problems of gossiping and broadcasting have been widely studied. The basic gossip problem is defined as follows: there are n individuals, with each individual having an item of gossip. The goal is to communicate each item of gossip to every other individual. Communication typically proceeds in rounds, with the objective of minimizing the number of rounds. One popular model, called the telephone call model, allows for communication to take place on any chosen matching between the individuals in each round. Each individual may send (receive) a single item of gossip in a round to (from) another individual. In the broadcasting problem, one individual wishes to broadcast an item of gossip to everyone else. In this paper, we study generalizations of gossiping and broadcasting. The basic extensions are: (a) each item of gossip needs to be broadcast to a specified subset of individuals and (b) several items of gossip may be known to a single individual. We study several problems in this framework that generalize gossiping and broadcasting. Our study of these generalizations was motivated by the problem of managing data on storage devices, typically a set of parallel disks. For initial data distribution, or for creating an initial data layout we may need to distribute data from a single server or from a collection of sources.

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“…Note that other models exist like store-and-forward model (where a vertex can only communicate with a neighbor at distance 1) or 1-port models (in which a vertex can send only one message): see the book [25] or the surveys [10], [16], [18]. In first approximation the number of rounds of a broadcasting scheme represents the time needed to realize the scheme.…”

Section: Figure 1 Scheme For H(5) In Two Communication Roundsmentioning

confidence: 99%