Abstract
In this paper, an interconnection model for parallel computation, the Cubemat, is proposed, and an efficient layout and data transmission operations on it are presented. The node connections of the Cubemat consist of binary cube and global bus connections. The binary-reflected Cubemat, in which nodes are placed in the binary-reflected order in two directions on a plane, contains explicit mesh connections or torus in the order of node positions. When the number of nodes is large, the layout of the binary-reflected Cubemat fills only 4/9ths of the space of the simple Cubemat where the nodes are embedded in two directions in the ascending order. Even though each hypercube terminal of nodes in the Cubemat can send and receive data in the same time, data transmission between nodes through global connections is more efficient than the hypercube connection for small quantities of data. This paper also presents a method of data transformation between the ascending order and the binary-reflected order which is performed in O(log n) time on the n-node Cubemat using hypercube connection.
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