The KIPS Transactions:PartA (정보처리학회논문지A)

Korea Information Processing Society (한국정보처리학회)
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Embedding a Mesh into a Crossed Cube

메쉬의 교차큐브에 대한 임베딩

  • 김숙연 (한경대학교 컴퓨터공학과)
  • Published : 2008.12.31
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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 $2{\times}2^m$ can be embedded into a crossed cube with dilation 1 and expansion 1 and a mesh of size $4{\times}2^m$ 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 $2^n{\times}2^m$ can be embedded into a crossed cube with dilation 1 and expansion $2^{n-1}$ where $n{\geq}1$ and $m{\geq}3$.

교차큐브는 병렬처리 시스템의 상호연결망으로서 널리 알려진 하이퍼큐브와 많은 면에서 비슷하면서도 절반 정도의 지름을 가지는 등 개선 된 망 성질들을 가지므로 각광 받아 왔다. 크기가 $2{\times}2^m$이거나 $4{\times}2^m$인 메쉬를 연장율 1로 교차큐브에 임베딩하는 연구 결과는 이미 발표된바 있다. 그러나 양변의 길이가 모두 8 이상인 메쉬가 교차큐브에 연장율 1로 임베딩되는지는 알려진 바가 없다. 본 논문에서는 크기 $2^n{\times}2^m$인 메쉬가 교차큐브에 연장율 1, 확장율 $2^{n-1}$로 임베딩될 수 있음을 보인다, $n{\geq}1$, $m{\geq}3$.

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