Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Embedding Algorithm among Folded Hypercube, Even Network and Odd Network

폴디드 하이퍼큐브와 이븐연결망, 오드연결망 사이의 임베딩 알고리즘

  • 김종석 (영남대학교 전자공학부) ;
  • 심현 (순천대학교 컴퓨터공학과) ;
  • 이형옥 (순천대학교 컴퓨터교육과)
  • Published : 2008.08.15
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Abstract

In this paper, we will analyze embedding among Folded Hypercube, Even Network and Odd Network to further improve the network cost of Hypercube. We will show Folded Hypercube $FQ_n$ can be embedded into Even Network $E_{n-1}$ with dilation 2, congestion 1 and Even Network $E_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 1. Also, we will prove Folded Hypercube $FQ_n$ can be embedded into Odd Network $O_{n-1}$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 2, congestion 1. Finally, we will show Even Network $E_d$ can be embedded into Odd Network $O_d$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $E_{d-1}$ with dilation 2, congestion 1.

본 논문에서는 하이퍼큐브보다 망비용이 개선된 폴디드 하이퍼큐브 연결망과 이븐연결망, 오드 연결망 사이의 임베딩을 분석한다. 연구 결과로 폴디드 하이퍼큐브 $FQ_n$을 이븐연결망 $E_{n-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보이고, 이븐연결망 $E_d$을 폴디드 하이퍼큐브 $FQ_{2d-3}$에 연장율 1에 임베딩 가능함을 보인다. 또한, 폴디드 하이퍼큐브 $FQ_n$는 오드연결망 $O_{n-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보이고, 오드연결망 $O_d$는 폴디드 하이퍼큐브 $FQ_{2d-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보인다. 마지막으로, 이븐연결망 $E_d$는 오드연결망 $O_d$에 연장을 2, 밀집을 1에 임베딩 가능함을 보이고, 오드연결망 $O_d$는 이븐연결망 $E_{d-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보인다.

Keywords

References

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