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

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Embedding Complete Binary Trees into Crossed Cubes

완전이진트리의 교차큐브에 대한 임베딩

  • 김숙연 (한경대학교 컴퓨터공학과)
  • Published : 2009.06.15
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Abstract

The crossed cube, a variation of the hypercube, possesses a better topological property than the hypercube in its diameter that is about half of that of the hypercube. It has been known that an N-node complete binary tree is a subgraph of an (N+1)-node crossed cube [P. Kulasinghe and S. Bettayeb, 1995]. However, efficient embedding methods have not been known for the case that the number of nodes of the complete binary tree is greater than that of the crossed cube. In this paper, we show that an N-node complete binary tree can be embedded into an M-node crossed cube with dilation 1 and load factor [N/M], N>M$\geq$2. The dilation and load factor is optimal. Our embedding has a property that the tree nodes on the same level are evenly distributed over the crossed cube nodes. The property is especially useful when tree-structured algorithms are processed on a crossed cube in a level-by-level way.

교차큐브는 하이퍼큐브의 변형으로서 하이퍼큐브의 절반정도의 지름을 가지는 등의 개선된 망 성질을 가진다. N-노드 완전이진트리는 (N+1)-노드 교차큐브의 부그래프임이 알려져 있으나 [P. Kulasinghe and S, Bettayeb, 1995] 완전이진트리의 노드 개수가 교차큐브의 노드 개수보다 더 큰 경우에 대한 효과적인 임베딩 방법은 알려져 있지 않다. 본 논문에서는 N-노드 완전이진트리를 N-노드 교차큐브에 연장을 1, 부하율 [N/M]로 임베딩할 수 있음을 보인다(N>M$\geq$2). 여기서 연장율과 부하율은 최적이다. 본 논문에서 제시하는 임베딩 방법은 같은 레벨의 트리 노드들을 교차큐브의 노드들에 골고루 분포시키는 특징도 가지고 있다. 이 특징은 트리 구조 알고리즘을 교차큐브에서 레벨 단위로 실행할 때 특히 유용하다.

Keywords

References

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