P. Fragopoulou and S. G. Akl. A framework for optimal communication on the multidimensional torus network. Technical Report 94-363, Dept. of Computing and Information Science, Queen's Univeristy, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are common in current generation systems. Hence, the result can be immediately used by modern parallel machines. Recently, some complete exchange algorithms have been proposed for multidimensional tori. However, these either use a direct model [18] or use a multi port store and forward model [7]. Due to the absence of any other known indirect complete exchange algorithm for tori, we compare our schemes with indirect complete exchange algorithms for meshes [2, 8, 16] Our algorithm only uses about half of the transmission time and half of the startup time, as opposed to the best known ....

P. Fragopoulou and S. G. Akl. A framework for optimal communication on the multidimensional torus network. Technical Report 94-363, Dept. of Computing and Information Science, Queen's Univeristy, 1994.

....is common in current generation systems. Hence, the result can be immediately used by modern parallel machines. Recently, some complete exchange algorithms have been proposed for multidimensional tori. However, these either use a direct model [10, 21] or use a multi port store and forward model [8]. We compare, using simulations, the performance of our indirect complete exchange algorithm for tori with the performance of the direct complete exchange algorithm for tori in [10] As can be expected, our indirect algorithm performs better than the direct algorithm when the messages are of ....

P. Fragopoulou and S. G. Akl. "A Framework for Optimal Communication on the Multidimensional Torus Network". Technical Report 94-363, Dept. of Computing and Information Science, Queen's Univeristy, 1994.

....to this, nodes obtained as rotations of each other are all at the same distance from node 0 n . 2 Lemma 3: If (v; u) is a directed edge of dimension g j i , then the 2n directed edges derived from (v; u) by consecutive applications of the rotation operation are all of different dimensions [10]. Proof: This is derived in a straightforward manner from the first part of lemma 2, which describes the impact of the rotation operation on the dimension of an edge. For example, for edge (01; 31) of MT 2;4 the 2n = 4 edges produced by consecutive applications of the rotation operation are (01; ....

.... : 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 [10]. For example, node 311331 of MT 6;4 , which belongs to a nonfull necklace that contains 4 nodes constists of the substring 31 of two digits which is repeated modified three times as follows: r 2 (3)r 2 (1)r(3)r(1)31 = 311331. From the properties of the rotation operation we conclude that the ....

P. Fragopoulou and S.G. Akl, "A Framework for Optimal Communication on the Multidimensional Torus Network", Technical Report no. 94-363, Department of Computing and Information Science, Queen's University, Kingston, ON, Canada, 1994.

.... on adaptive communication algorithms on the generalized hypercube network can be found in [14] The method of spanning graph construction has been previously used to design communication algorithms on other interconnection networks, such as the binary hypercube [16] the multidimensional torus [10], and the star network [6, 7] 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 generalized ....

P. Fragopoulou and S.G. Akl, "A Framework for Optimal Communication on the Multidimensional Torus Network", Technical Report no. 94-363, Department of Computing and Information Science, Queen's University, Kingston, ON, Canada, 1994.

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