Embedding a Mesh of Size 2n×2m Into a Twisted Cube


The KIPS Transactions:PartA, Vol. 16, No. 4, pp. 223-226, Aug. 2009
10.3745/KIPSTA.2009.16.4.223,   PDF Download:

Abstract

The twisted cube has received great attention as an interconnection network of parallel systems because it has several superior properties, especially in diameter, to the hypercube. It was recently known that, for even m , a mesh of size 2× 2m can be embedded into a twisted cube with dilation 1 and expansion 1 and a mesh of size 4 × 2m with dilation 1 and expansion 2 [Lai and Tsai, 2008]. However, as we know, it has been a conjecture that a mesh with more than eight rows and columns can be embedded into a twisted cube with dilation 1. In this paper, we show that a mesh of size 2ⁿ × 2m can be embedded into a twisted cube with dilation 1 and expansion 2n?1 for even m and with dilation 1 and expansion 2n for odd m where 1≤ n ≤ m.


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Cite this article
[IEEE Style]
S. Y. Kim, "Embedding a Mesh of Size 2n×2m Into a Twisted Cube," The KIPS Transactions:PartA, vol. 16, no. 4, pp. 223-226, 2009. DOI: 10.3745/KIPSTA.2009.16.4.223.

[ACM Style]
Sook Yeon Kim. 2009. Embedding a Mesh of Size 2n×2m Into a Twisted Cube. The KIPS Transactions:PartA, 16, 4, (2009), 223-226. DOI: 10.3745/KIPSTA.2009.16.4.223.