Embedding binary trees into crossed cubes

Kulasinghe, P.; Bettayeb, Saïd

doi:10.1109/12.392850

Cited by 100 publications

(65 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Many graph embeddings take cycles, trees, meshes, paths, etc., as guest graphs [3], [10], [12], [14], [16], [21], [22] because these interconnection networks are widely used in parallel computing systems. Path embeddings are especially important because paths are the common structures used to model linear arrays in parallel processing [5], [6], [17], [18], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Optimal Embeddings of Paths with Various Lengths in Twisted Cubes

Fan

Jia

Lin

2007

IEEE Trans. Parallel Distrib. Syst.

View full text Add to dashboard Cite

Abstract-Twisted cubes are variants of hypercubes. In this paper, we study the optimal embeddings of paths of all possible lengths between two arbitrary distinct nodes in twisted cubes. We use T Q n to denote the n-dimensional twisted cube and use distðT Q n ; u; vÞ to denote the distance between two nodes u and v in T Q n , where n ! 1 is an odd integer. The original contributions of this paper are as follows: 1) We prove that a path of length l can be embedded between u and v with dilation 1 for any two distinct nodes u and v and any integer l with distðT Q n ; u; vÞ þ 2 l 2 n À 1 ðn ! 3Þ and 2) we find that there exist two nodes u and v such that no path of length distðT Q n ; u; vÞ þ 1 can be embedded between u and v with dilation 1 ðn ! 3Þ. The special cases for the nonexistence and existence of embeddings of paths between nodes u and v and with length distðT Q n ; u; vÞ þ 1 are also discussed. The embeddings discussed in this paper are optimal in the sense that they have dilation 1.

show abstract

Section: Introductionmentioning

confidence: 99%

Optimal Embeddings of Paths with Various Lengths in Twisted Cubes

Fan

Jia

Lin

2007

IEEE Trans. Parallel Distrib. Syst.

View full text Add to dashboard Cite

show abstract

“…[3,6,7,8,9,11,13]. 따 라서 최단경로, 헤밀톤 경로, 사이클, 트리, 메쉬 등을 교차큐 브에 임베딩하는 연구도 활발히 진행되었다 [3,6,12,19,14,10,5]. …”

unclassified

Embedding a Mesh into a Crossed Cube

Kim¹

2008

The KIPS Transactions:PartA

View full text Add to dashboard Cite

키워드 : 교차큐브, 메쉬, 임베딩, 연장율, 확장율 Embedding a Mesh into a Crossed CubeKim, Sook-Yeon † ABSTRACTThe 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 m 2 2 × can be embedded into a crossed cube with dilation 1and expansion 1 and a mesh of size m 2 4 × 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

show abstract

“…It is important to study the problem of how to embed different kinds of trees into a host graph. Recently, many tree embedding problems have been studied [9], [7], [10].…”

Section: Introductionmentioning

confidence: 99%

Embedding Complete Binary Trees into Locally Twisted Cubes

Han¹,

Fan²,

You

et al. 2012

AEF

View full text Add to dashboard Cite

Abstract. The locally twisted cube is a newly introduced interconnection network for parallel computing, which possesses many desirable properties. In this paper, the problem of embedding complete binary trees into locally twisted cubes is studied. Let LT Q n (V, E) denote the n-dimensional locally twisted cube. We find the following result in this paper: for any integer n ≥ 2, we show that a complete binary tree with 2 n − 1 nodes can be embedded into the LT Q n with dilation 2.

show abstract

Embedding binary trees into crossed cubes

Cited by 100 publications

References 13 publications

Optimal Embeddings of Paths with Various Lengths in Twisted Cubes

Optimal Embeddings of Paths with Various Lengths in Twisted Cubes

Embedding a Mesh into a Crossed Cube

Embedding Complete Binary Trees into Locally Twisted Cubes

Contact Info

Product

Resources

About