Sook Yeon Kim

The KIPS Transactions:PartA, Vol. 15, No. 6, pp. 301-308, Dec. 2008
10.3745/KIPSTA.2008.15.6.301,   PDF Download:

Abstract

The crossed cube has received great attention because it has equal or superior properties to the hypercube that is widely known as a versatile parallel processing system. It has been known that a mesh of size 2 × 2^m can be embedded into a crossed cube with dilation 1 and expansion 1 and a mesh of size 4× 2^m with dilation 1 and expansion 2. However, as we know, it has been a conjecture that a mesh with more than eight rows and columns can be embedded into a crossed cube with dilation 1. In this paper, we show that a mesh of size 2^n × 2^m can be embedded into a crossed cube with dilation 1 and expansion 2^n?1 where n ≥1 and m ≥ 3 .

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