P. Berthome, A. Ferreira, and S. Perennes, "Decomposing Hierarchical Cayley Graphs, with Applications to Information Dissemination and Algorithm Design", In Proc. Fifth IEEE Symp. on Parallel and Distr. Comput. , 1993, 720--723.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... star graph has been subject of extensive studies: its topological properties have been analysed in [9, 11, 33, 36] its fault tolerance has been studied in [2, 3, 13, 17, 19, 25, 28] the problem of designing parallel algorithms for star graph based interconnection networks has been studied in [5, 6, 7, 12, 26, 29, 30, 34]. In this paper we give new results on the fault tolerance capabilities of the star graph. We first consider in Section 3 the problem of determining the maximum number r(n) of vertices in an n vertices star graph S n such that by removing any set of vertices and or edges from S n , of ....

P. Berthome, A. Ferreira, and S. Perennes, "Decomposing Hierarchical Cayley Graphs, with Applications to Information Dissemination and Algorithm Design", In Proc. Fifth IEEE Symp. on Parallel and Distr. Comput. , 1993, 720--723.

....Theorem 2.3.1. For general fixed degree, other constructions of networks with efficient broadcasting schemes are given in [CGV89] Broadcasting (and also gossiping) in the lately proposed star graph and pancake graph (as special csaes of Cayley graphs, see [AK89, ABR90] has been investigated in [MS90b, BFP92, Go92] where efficient broadcast schemes are presented. The star graph and pancake graph have become very popular because they have a very regular interconnection pattern, sublogarithmic degree and diameter. 3 GOSSIPING 3.1 Introduction This section is devoted to the gossip problem. Unlike the ....

P. Berthom'e, A. Ferreira, S. Perennes, "Decomposing hierarchical Cayley graphs, with applications to information dissemination and algorithm design", Technical Report 92-38, Ecole Normale Sup'erieure de Lyon, 1992.

....algorithms the assumption that each node can exchange messages of fixed length with all of its neighbors at each time step, i.e. the all port communication assumption, is adapted. Communication is assumed to be bidirectional. Other data communication algorithms and properties on Sn can be found in [1, 4, 5, 13, 14, 22, 25, 26, 27]. Fault tolerant algorithms and properties on Sn using different approaches can be found in [2, 8, 9, 17, 19, 29] This paper is organized as follows: Following the introduction to the subject in section 1, notations and definitions that are used throughout the paper are introduced in section 2. ....

P. Berthom'e, A. Ferreira, and S. Perennes, "Decomposing Hierarchical Cayley Graphs, with Applications to Information Dissemination and Algorithm Design", Technical Report no. 92-32, Laboratoire de l' Informatique du Parall'elism, Ecole Normale Superi'eure de Lyon, Lyon, France, 1992.

.... hypercube [11, 16] However it is the first time they are considered on the star graph (defined below) The multinode broadcasting problem on the star graph under the assumption that messages of arbitrary length can be exchanged between two adjacent processors at each time step has been studied in [9, 20]. Another class of spanning trees, called edge disjoint spanning trees, that reduce the communication time of the single node broadcasting problem on the star network and offer many applications in the area of fault tolerant communication algorithms have been constructed in [14] The problem of ....

.... broadcasting problem on the star network and offer many applications in the area of fault tolerant communication algorithms have been constructed in [14] The problem of generalized routing on star graphs was first addressed in [23] Other communication algorithms on the star graph can be found in [1, 7, 9, 20, 25, 26, 30]. a b b c d d c a 1234 4231 1324 4321 3412 2413 3214 2314 4312 1342 3421 1423 4123 4132 1432 3124 2134 3241 2341 4213 1243 3142 2143 2431 123 132 321 231 312 213 (a) b) Figure 1: The 4 star: 4 interconnected 3 stars The n star graph, denoted by Sn , has n nodes. Each of the nodes is labeled ....

P. Berthom'e, A. Ferreira, and S. Perennes, "Decomposing Hierarchical Cayley Graphs, with Applications to Information Dissemination and Algorithm Design", Technical Report no. 92-32, Laboratoire de l' Informatique du Parallelism, Ecole Normale Sup'erieure de Lyon, Lyon, France, July 1992.

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