• Journal of KIISE:Computer Systems and Theory
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• v.27 no.2
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• pp.169-176
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• 2000

This paper is considered with the problem of embedding complete binary trees into 3-dimensional meshes using dimension-ordered routing with primary concern of minimizing link congestion. The authors showed that a complete binary tree with $2^P-1$ nodes can be embedded into a 3-dimensional mesh with optimum size, $2^P$ nodes, if the link congestion is two[14], (More precisely, the link congestion of each dimension is two, two, and one if the dimension-ordered routing is used, and two, one, and one if the dimension-ordered routing is not imposed.) In this paper, we present a scheme to find an embedding of a complete binary tree into a 3-dimensional mesh of size no larger than 1.27 times the optimum with link congestion one while using dimension-ordered routing.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.7_8
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• pp.381-386
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• 2003

In this paper, we consider the problem of embedding complete binary trees into 3-dimensional meshes. The method of embedding a complete binary tree into 3-dimensional mesh with the link congestion two is considered in [1], and the embedding in [2] shows that a complete binary tree can be embedded into a ,3-dimensional mesh of expansion 1.27. The proposed embedding in this paper shows that a complete binary tree can be embedded into a 3-dimensional mesh of expansion approximately 1.125 with the link congestion one, using the dimensional ordered routing. Such method yields some improved features in terms of minimizing the link congestion or the expansion of embedding comparing to the previous results.