Embedding Methods for Bubble-Sort, Pancake, and Matrix-Star Graphs

Kim, Jong-Seok; Kim, Mi-Hye; Sim, Hyun Sub; Lee, Hyeong-Ok

doi:10.1007/978-3-642-20975-8_27

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One Of the Important Interconnection Network1

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2014

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“…into it with expansion 1 and dilation 7. Also, the average dilation of the star graph S 2n is smaller than 3 and the bubble sort graph B 2n is smaller than 4 [5,11]. This paper analyzes an embedding algorithm from a matrix-star graph MS 2,n to a transposition graph T 2n .…”

Section: One Of the Important Interconnection Networkmentioning

confidence: 99%

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An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph

Kim¹,

Lee²

2014

Journal of the Korea Institute of Information and Communication

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The matrix-star and the transposition graphs are considered as star graph variants that have various merits in graph theory such as node symmetry, fault tolerance, recursive scalability, etc. This paper describes an one-to-one mapping algorithm from a matrix-star graph to a transposition graph using adjacent properties in graph theory. The result show that a matrix-star graph MS 2,n can be embedded in a transposition graph T 2n with dilation n or less and average dilation 2 or less.

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Section: One Of the Important Interconnection Networkmentioning

confidence: 99%

“…Fig. 2shows an example of MS 2,2 , in which the nodes are represented by 2×2 matrices[11]. The terms node and matrix are interchangeably used in this paper because a node is expressed by a matrix.…”

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confidence: 99%