The KIPS Transactions:PartA (정보처리학회논문지A)

Korea Information Processing Society (한국정보처리학회)
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Embedding Algorithm between [ 22n-k×2k] Torus and HFN(n,n), HCN(n,n)

[ 22n-k×2k] 토러스와 HFN(n,n), HCN(n,n) 사이의 임베딩 알고리즘

  • 김종석 (오클라호마 주립대학교 컴퓨터과학과) ;
  • 강민식 ((주)보고정보 기획영업팀)
  • Published : 2007.12.31
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Abstract

In this paper, we will analysis embedding between $2^{2n-k}{\times}2^k$ torus and interconnection networks HFN(n,n), HCN(n,n). First, we will prove that $2^{2n-k}{\times}2^k$ torus can be embedded into HFN(n,n) with dilation 3, congestion 4 and the average dilation is less than 2. And we will show that $2^{2n-k}{\times}2^k$ torus can be embedded into HCN(n,n) with dilation 3 and the average dilation is less than 2. Also, we will prove that interconnection networks HFN(n,n) and HCN(n,n) can be embedded into $2^{2n-k}{\times}2^k$ torus with dilation O(n). These results mean so many developed algorithms in torus can be used efficiently in HFN(n,n) and HCN(n,n).

본 논문에서는 $2^{2n-k}{\times}2^k$ 토러스 연결망과 상호연결망 HFN(n,n)과 HCN(n,n) 사이의 임베딩을 분석한다. 먼저, $2^{2n-k}{\times}2^k$ 토러스를 HFN(n,n)에 연장율 3과 밀집율 4로 임베딩 가능함을 보이며, 평균연장율이 2 이하임을 증명한다. 그리고 $2^{2n-k}{\times}2^k$ 토러스를 HCN(n,n)에 연장율 3으로 임베딩 가능함을 보이며, 평균 연장율이 2 이하임을 증명한다. 또한 HFN(n,n)과 HCN(n,n)이 $2^{2n-k}{\times}2^k$ 토러스에 임베딩하는 연장율이 O(n)임을 보인다. 이러한 결과는 토러스에서 개발된 여러 가지 알고리즘을 HCN(n,n)과 HFN(n,n)에서 효율적으로 이용할 수 있음을 의미한다.

Keywords

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