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

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Link-Disjoint Embedding of Complete Binary Trees into 3D-Meshes using Dimension-Ordered Routing

순위차원라우팅을 사용한 완전 이진트리의 3차원 메쉬로의 링크 충돌 없는 임베딩

  • 박상명 (숙명여자대학교 자연과학연구소) ;
  • 이상규 (숙명여자대학교 전산학과) ;
  • 문봉희 (숙명여자대학교 전산학과)
  • Published : 2000.02.15
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Abstract

This paper is considered with the problem of embedding complete binary trees into 3-dimensional meshes using dimension-ordered routing with primary concern of minimizing link congestion. The authors showed that a complete binary tree with $2^P-1$ nodes can be embedded into a 3-dimensional mesh with optimum size, $2^P$ nodes, if the link congestion is two[14], (More precisely, the link congestion of each dimension is two, two, and one if the dimension-ordered routing is used, and two, one, and one if the dimension-ordered routing is not imposed.) In this paper, we present a scheme to find an embedding of a complete binary tree into a 3-dimensional mesh of size no larger than 1.27 times the optimum with link congestion one while using dimension-ordered routing.

본 논문에서는 령크 충돌을 최소화 하는데 중점을 두고 순위차원 라우팅을 사용하여 완전이진트리를 3차원 메쉬로 임베딩하는 방법을 제안한다. 기존의 연구[14]에서는, 완전이진트리를 3차원 메쉬에 임베딩 할 때 순위차원 라우팅을 사용하는 경우 1, 2 차원에서 링크 충돌이 발생하였고, 순위차원 라우팅을 따르지 않는 경우 1차원에서만 링크 충돌이 존재하도록 하는 임베딩 방법을 보였었다. 이와 비교하여 본 논문에서는 순위차원 라우팅을 사용하고 링크 충돌이 존재하지 않는 임베딩 방법을 제안하며, 이 방법에 의해 임베딩을 수행한 결과, 임베딩을 위해 사용된 메쉬의 크기가 최적크기의 1.27 배를 넘지 않음을 증명한다.

Keywords

References

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