P. Fragopoulou, S. G. Akl, and H. Meijer, "Optimal Communication Primitives on the Generalized Hypercube Network," Journ. Paral. Distr. Comput. 32, 1996, pp. 173-187.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....scheduling is the consequence of data flow. We introduce a heuristic path driven scheduling and mapping algorithm (P D) in this paper to obtain the optimized task clusters according to data flows and map them onto the Processing Elements (PEs) of a target machine, the generalized hypercube [1] [4], 14] heuristically. The rest of the paper is organized as follows. The P D scheduling algorithm is described in Section 2. In Section 3, we discuss the mapping on the PEs of the generalized hypercube. Simulation results are given in Section 4. Finally conclusions are presented in Section 5. 2 ....

P. Fragopoulou, S. G. Akl and H. Meijer, Optimal communication Primitives on the Generalized Hypercube Network Journal of Parallel and Distributed Computing, 32, 173-187, 1996.

....for a total of n (k 1) neighbors per node. The n D GH(k,n) has diameter equal to only n. The increased VLSI cost of GHs results in outstanding performance that permits optimal emulation of hypercubes and k ary n cubes, and efficient implementation of complex communications patterns [2, 4]. 2 HOW Architectures We propose in this paper a new class of architectures, namely HOWs (Highly Overlapping Windows) that can be implemented effectively with current technology, contain many highly overlapping GHs, are scalable, and possess outstanding topological properties. HOWs require fewer ....

P. Fragopoulou, S. G. Akl, and H. Meijer, "Optimal Communication Primitives on the Generalized Hypercube Network," Journ. Paral. Distr. Comput. 32, 1996, 173-187.

....the function does not refer to a knowledge of the elements of A, but can evaluate connectivity based on the origin and terminus. Such functions are frequently used in defining the algebraic graphs used in multiprocessor computers. Examples of such graphs are Cayley graphs [7] including hypercube [5] and [8] and de Bruijn networks [13] A routing function F R : V x V P is a function that defines a path in a graph G for any two vertices. An interconnection network, I N , is a triplet (G, F C , F R ) where G is a graph, F C is a connectivity function of G and F R is the routing function that ....

Fragopoulou, P. and S.G. Akl. Optimal communication primitives on the generalized hypercube network. Journal of Parallel Distributed Computing. 32:173-87, 1996.

.... hypercube (with congestion and dilation one) any permutation can be off line routed in 2 log d N Gamma 1 steps [308] Optimal algorithms for multinode broadcasting, single node scatter, and total exchange on the generalized hypercube are again based on multiple edge disjoint spanning trees [79]. 5 The Star Graph Let X = f1; 2; ng where n 2. Let S n be the set of all possible permutations over X. Then, S n forms a permutation group, known as symmetric group. A set Omega is said to be a set of generators for group Gamma, if by applying the elements of Omega repeatedly, we ....

Fragopoulou, P., Akl, S. G., and Meijer, H. Optimal communication primitives on the generalized hypercube network. J. Parallel Distrib. Comput. 32 (2), 1996, pp. 173--187.

.... algorithms on the MT n;k network under a variety of communication models can be found in [11] The method of spanning graph construction has been previously used to design communication algorithms on other interconnection networks, such as the binary hypercube [16, 4] the generalized hypercube [9], and the star [6, 7] networks. The remainder of this paper is organized as follows. Notations and definitions that are used throughout the paper are introduced in section 2. Sections 3 and 4 present the construction of a spanning tree and a spanning graph, respectively, on the multidimensional ....

P. Fragopoulou, S.G. Akl, and H. Meijer, "Optimal Communication Primitives on the Generalized Hypercube Network", Technical Report no. 94-362, Department of Computing and Information Science, Queen's University, Kingston, ON, Canada, 1994.

.... : v 1 v 0 (m is a divisor of n) which is repeated m times with its nonzero digits modified as follows: r m Gamma1 (v n m Gamma1 ) r m Gamma1 (v 1 )r m Gamma1 (v 0 ) r i (v n m Gamma1 ) r i (v 1 )r i (v 0 ) r(v n m Gamma1 ) r(v 1 )r(v 0 )v n m Gamma1 : v 1 v 0 [9]. For example, node 330220 of GH 6;4 which belongs to a nonfull necklace that contains 12 nodes constists of the substring 220 of three digits which is repeated twice as follows: r(2)r(2)r(0)220 = 330220. From the properties of the rotation operation we conclude that the nodes of GH n;k at each ....

....D(v) i Gamma 1 in the (i Gamma 1) st subtree of BST 0 is obtained by changing to zero its first nonzero digit cyclically to the left of position (n Gamma 1 Gamma (i Gamma 1) mod n. The digit that is changed into zero in R(v) is in position (p 1) mod n and its parent is node R(u) [9]. For example, node 103302 of GH 6;4 has dispacement 2, and its parent node in the second subtree of BST 0 is obtained by changing to zero its first nonzero digit cyclically to the left of position 3. As a consequence its parent is node 003302. Node R(103302) 033022 has dispacement 1 and its ....

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P. Fragopoulou, S.G. Akl, and H. Meijer, "Optimal Communication Primitives on the Generalized Hypercube Network", Technical Report, no. 94-362 Department of Computing and Information Science, Queen's University, Kingston, ON, Canada, 1994.

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P. Fragopoulou, S.G. Akl, and H. Meijer. Optimal communication primitives on the generalized hypercube network. Journal of Parallel and Distributed Computing, Vol. 32, 1996, pp. 173--187.

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P. Fragopoulou, S. G. Akl, and H. Meijer, "Optimal Communication Primitives on the Generalized Hypercube Network," Journ. Paral. Distr. Comput. 32, 1996, pp. 173-187.

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Fragopoulou, P., Akl, S. G. and Meijer, M. (1996) Optimal communication primitives on the generalized hypercube network. J. Parallel Distrib. Comput., 32, 173--187.

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P. Fragopoulou, S.G. Akl, H. Meijer, Optimal communication primitives on the generalized hypercube network, J. Parallel Distrib. Comput. 32 (1996) 173--187.

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