Fraigniaud, P, Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers, IEEE Transaction on Computers, 41(11), November 1992, pages 1410-1419.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....message to transmit to all other nodes of the network. A k fault tolerant all to all broadcasting process is one which sends the messages out with enough redundancy so that the broadcasting can be completed even if k nodes has failed. Two different models of communications, shouting and whispering[5] are considered. In the shouting model, a node can communicate simultaneously with all the adjacent nodes. That is, each node has all port capability. In the whispering model, a node can only communicate with one adjacent node at any given time. Each node has one port capability. We assume that ....

....that requires only 1.88d steps. Since then, a lot of papers like Scott s[13] Petrini s[10] and Johnsson s[8] were published about allto all broadcasting in hypercubes. However, very few of them deal with all to all broadcasting when some nodes or links may have already failed. Fraigniaud[5] proposed a asymptotically optimal k fault tolerant all to all broadcasting scheme for d dimensional hypercubes where 0 k d. His scheme is based on Johnsson and Ho s[8] arc disjoint spanning tree. Let the time to send out a message be T = # F # [8] # is the start up time. # is the time to ....

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Fraigniaud, P, Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers, IEEE Transaction on Computers, 41(11), November 1992, pages 1410-1419.

....call it all port communication. If a processor can only send and receive on one of its ports at any time, and the ports on which a processor sends and receives can be different [16] it is called one port communication. In this paper we adopt the model of communication cost proposed by Fraigniaud [11, 12]. The time T required for sending a message from one processor to one of its neighboring processors is assumed to be the sum of a start up time # and a propagation time L # proportional to the length of messages L (1 # is the bandwidth) i.e. T = # L # . This evaluation model is said to be ....

.... nodes are deleted from G, the resulting subgraph is still connected (strongly connected) 2] An algorithm for communicating in a digraph D(V, A) can tolerate f faults if and only if each data element can be routed through at least f 1 node disjoint paths from its source to its destination [11]. It has been proven by Edmonds [10] that every digraph possesses as many arc disjoint spanning trees rooted at any node as the arc connectivity of the digraph. Here, for a digraph D = V, A) arc connectivity represents the minimum number of elements in an arc set A such that D = V, A A ) ....

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P. Fraigniaud, "Asymptotically optimal broadcasting and gossiping in faulty hypercube multicomputers," IEEE Transactions on Computers, Vol. 41, 1992, pp. 1410-1419.

....of hypercube networks with faults was considered in [10, 11] Many This work is supported in part by the National Science Foundation under Grant CCR 0000206. fault tolerant communication algorithms concentrating on one to one routing or broadcasting in hypercube networks have been proposed [2, 4, 6, 7, 12, 13, 16, 17]. A network G of degree d is said strongly fault tolerant [15] if with at most d 2 faulty nodes, any two nodes u and v in G are connected by minfdeg f (u) deg f (v)g nodedisjoint paths, where deg f (u) and deg f (v) are the numbers of non faulty neighbors of the nodes u and v in G, respectively. ....

P. Fraigniaud, "Asymptotically optimal broadcasting and gossiping in faulty hypercube multicomputers", IEEE Trans. Computers 41, 1992, pp. 1410-1419.

....and the survival graph. In either case, only structural aspects of the graph representing the interconnection network of the machine is taken into account. For other references the reader can look at the special issue on fault tolerance of IEEE Transaction on Computers, April 1990, and at [21] for references on communication with faults. 1.6.3.1 Vulnerability A first approach to the determination of the capacity of a network to tolerate faults is the study of the changes in the diameter of the graph when edges or vertices are deleted. We can consider what can be called a Menger ....

P. Fraigniaud. Asymptotically optimal broadcasting and gossiping in faulty hypercubes multicomputers. IEEE Transactions on Computers, 41(11):1410--1419, 1992.

.... then permutation routing can be performed in O(n) steps using queues of size O(n) with high probability [103] Problem 16 Do any constant degree networks share the above property Many fault tolerant algorithms have been proposed for global hypercube communication and especially broadcasting [26, 39, 81, 83, 107, 108, 173, 240, 266, 329]. Most algorithms exploit the multiplicity of hypercube paths by using extensively packet replication. 4.4 Dynamic Routing Problems Every node of the n dimensional hypercube independently generates packets with rate . Each packet s destination is chosen randomly, with each node at distance r ....

Fraigniaud, P. Asymptotically optimal broadcasting and gossiping in faulty hypercubes multicomputers. IEEE Trans. Comput. C-41 (11), 1992, pp. 1410--1419.

....to all members of the network. A k fault tolerant broadcast is to broadcast with enough redundancy so that the broadcast can be completed even if k links or nodes fail. The broadcast is carried out by a series of calls between nodes. Two different models of communication, shouting and whispering [3] are considered. In the shouting model, a node can communicate simultaneously with all the adjacent nodes. In the whispering model, a node can only communicate with one adjacent node at any given time. In this paper, we assume that the communications are based on a message passing procedure and ....

....[8] information dispersal algorithm to send out the message in m k pieces. A node can reconstruct the message if it receives m pieces of the message. They compared their scheme with schemes that send out k 1 copies of the message. They concluded that their scheme required less time. Fraigniaud [3] proposed optimal d 1 fault tolerant broadcasting schemes for d dimensional hypercubes. His algorithm is based on Johnsson and Ho s [7] arc 496 disjoint spanning tree. His scheme is optimal for short messages for both the shouting and whispering model. Moreover, his scheme is also sub optimal ....

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Fraigniaud, P. Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers. IEEE Transaction on Computers 41(12):1410-1419, Dec, 1992.

....non adjacent link and or vertex failures. Bienstock considered broadcasting in a model in which each edge is independently faulty with probability p [4] Pelc [18] has studied a model in which both nodes and calls can fail. Several other papers have investigated broadcasting in faulty hypercubes [5, 10, 11, 20]. For a survey of work on broadcasting and related problems, see [14] 2 Definitions Given a graph G = V; E) the k reliable broadcast time of a vertex u of G, denoted t k (u) is the minimum time required to guarantee broadcast from u in the presence of up to k transmission failures. The ....

P. Fraigniaud, Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers, IEEE Trans. Comp., to appear.

....From Menger s theorems [27] the vertex connectivity (resp. arc connectivity) is equal to the minimum, taken over all pairs (x; y) of vertices, of the maximum number of vertex disjoint (resp. arc disjoint) paths from x to y. High connectivity is related to the ability of tolerating faults [10], and to 8 provide high communication performances [25] We will see later that the high connectivity of f Q FKL n ; n 4g gives to this family about the same communication power [25] as the undirected hypercubes fQ n ; n 4g. For any digraph G = V; A) and for any vertex x 2 V , we ....

....one of the best known networks from a communication point of view. Among many other interesting properties, it is both a minimum broadcast graph [2] and a minimum gossip graph [23] It also o ers high communication performances under the linear cost model (see [17] and [30] even if faults occur [10, 11, 13, 29]. In this section, we show that the communication performances of the hypercube are not destroyed by our orientation, and that Q FKL n o ers almost the same communication behavior as Q n . We consider two classical measures for communication performances: the constant cost model, and the ....

P. Fraigniaud. Asymptotically optimal broadcasting and gossiping in faulty hypercubes multicomputers. IEEE Transactions on Computers, 41(11):1410-1419, 1992.

....by the routing in order to form the new headers which will be attached to the k copies of the message. The different copies are sent through the selected output channels. This is a long, but non exhaustive list For instance, there exists a lot of techniques for fault tolerant routing (see [34]) Some of them use tricky algorithms which cannot be modeled using any of the previously listed types of routing functions. Actually, the question is: what kind of information does the router need to route messages Our answer is that the routing decision depends on two parameters only: the ....

P. Fraigniaud, Asymptotically optimal broadcasting and gossiping in faulty hypercubes multicomputers, IEEE Transactions on Computers, 41 (1992), pp. 1410--1419.

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P. Fraigniaud. Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers. IEEE Trans. Comput., 41(11):1410{ 1419, 1992.

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