• Title/Summary/Keyword: Half Pancake Graphs

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One-to-One Mapping Algorithm between Matrix Star Graphs and Half Pancake Graphs (행렬스타 그래프와 하프 팬케익 그래프 사이의 일대일 사상 알고리즘)

  • Kim, Jong-Seok;Yoo, Nam-Hyun;Lee, Hyeong-Ok
    • Journal of the Korean Institute of Intelligent Systems
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    • v.24 no.4
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    • pp.430-436
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    • 2014
  • Matrix-star and Half-Pancake graphs are modified versions of Star graphs, and has some good characteristics such as node symmetry and fault tolerance. This paper analyzes embedding between Matrix-star and Half-Pancake graphs. As a result, Matrix-star graphs $MS_{2,n}$ can be embedded into Half-Pancake graphs $HP_{2n}$ with dilation 5 and expansion 1. Also, Half Pancake Graphs, $HP_{2n}$ can be embedded into Matrix Star Graphs, $MS_{2,n}$ with the expansion cost, O(n). This result shows that algorithms developed from Star Graphs can be applied at Half Pancake Graphs with additional constant cost because Star Graphs, $S_n$ is a part graph of Matrix Star Graphs, $MS_{2,n}$.

Analysis of Various Characteristics of the Half Pancake Graph (하프팬케익 그래프의 다양한 성질 분석)

  • Seo, Jung-Hyun;Lee, HyeongOk
    • Journal of Korea Multimedia Society
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    • v.17 no.6
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    • pp.725-732
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    • 2014
  • The Pancake graph is node symmetric and useful interconnection network in the field of data sorting algorithm. The Half Pancake graph is a new interconnection network that reduces the degree of the Pancake graph by approximately half and improves the network cost of the Pancake graph. In this paper, we analyze topological properties of the Half Pancake graph $HP_n$. Fist, we prove that $HP_n$ has maximally fault tolerance and recursive scalability. In addition, we show that in $HP_n$, there are isomorphic graphs of low-dimensional $HP_n$. Also, we propose that the Bubblesort $B_n$ can be embedded into Half Pancake $HP_n$ with dilation 5, expansion 1. These results mean that various algorithms designed for the Pancake graph and the Bubble sort graph can be executed on $HP_n$ efficiently.