• The KIPS Transactions:PartA
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• v.14A no.5
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• pp.263-268
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• 2007

In this paper, we analyze some topological properties of Folded Hyper-Star FHS(2n,n). First, we prove that FHS(2n,n) has maximal fault tolerance, and broadcasting time using double rooted spanning tree is 2n-1. Also we show that FHS(2n,n) can be embedded into Folded hypercube with dilation 1, and Folded hypercube can be embedded into FHS(2n,n) ith dilation 2 and congestion 1.

• Proceedings of the Korea Information Processing Society Conference
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• 2000.10a
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• pp.637-640
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• 2000

본 논문에서는 하이퍼큐브보다 망비용이 개선된 HFN(n,n)과 2n-hypercube 사이의 임베딩을 분석한다. 2n-hypercube를 HFN(n,n)에 연장율 3에 임베딩 가능함을 보이고, HFN(n,n)을 2n-hypercube에 임베딩하는 비용이 O(n)임을 보인다.

• KIPS Transactions on Computer and Communication Systems
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• v.2 no.4
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• pp.151-154
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• 2013

In this paper, we will analyze embedding between Folded Hypercube and HFH. We will show Folded Hypercube $FQ_{2n}$ can be embedded into HFH($C_n,C_n$) with dilation 4, expansion $\frac{(C_n)^2}{2^{2n}}$ and HFH($C_d,C_d$) can be embedded into $FQ_{4d-2}$ with dilation O(d).

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.7
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• pp.318-326
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• 2008

In this paper, we will analyze embedding among Folded Hypercube, Even Network and Odd Network to further improve the network cost of Hypercube. We will show Folded Hypercube $FQ_n$ can be embedded into Even Network $E_{n-1}$ with dilation 2, congestion 1 and Even Network $E_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 1. Also, we will prove Folded Hypercube $FQ_n$ can be embedded into Odd Network $O_{n-1}$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 2, congestion 1. Finally, we will show Even Network $E_d$ can be embedded into Odd Network $O_d$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $E_{d-1}$ with dilation 2, congestion 1.

• Journal of Korea Multimedia Society
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• v.11 no.9
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• pp.1227-1237
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• 2008

In this paper, we analyze topological properties and embedding of Folded Hyper-Star network to further improve the network cost of Hypercube, a major interconnection network. Folded Hyper-Star network has a recursive expansion and maximal fault tolerance. The result of embedding is that Folded Hypercube $FQ_n$ and $n{\times}n$ Torus can be embedded into Folded Hyper-Star FHS(2n,n) with dilation 2. Also, we show Folded Hyper-Star FHS(2n,n) can be embedded into Folded Hypercube $FQ_{2n-1}$ with dilation 1.

• The KIPS Transactions:PartA
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• v.16A no.4
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• pp.299-306
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• 2009

Hierarchical Folded HyperStar Network has lower network cost than HCN(n,n) and HFN(n,n) which are hierarchical networks with the same number of nodes. In this paper, we analyze embedding between Hierarchical Folded HyperStar HFH($C_n,C_n$) and Hypercube, HCN(n,n), HFN(n,n). The results of embedding are that HCN(n,n), HFN(n,n) and Hypercube $Q_{2n}$ can be embedded into HFH($C_n,C_n$) with expansion $\frac{C^n}{2^{2n}}$ and dilation 2, 3, and 4, respectively. Also, HFH($C_n,C_n$) can be embedded into HFN(2n,2n) with dilation 1. These results mean so many developed algorithms in Hypercube, HCN(n,n), HFN(n,n) can be used efficiently in HFH($C_n,C_n$).

• Proceedings of the Korea Information Processing Society Conference
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• 2007.11a
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• pp.663-666
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• 2007

본 논문에서는 하이퍼큐브보다 망비용이 개선된 Folded 하이퍼큐브 연결망과 오드 연결망 사이의 임베딩을 분석한다. Folded 하이퍼큐브 $FQ_n$을 오드 연결망 $O_{2n+1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보이고, 오드 연결망 $O_d$을 Folded 하이퍼큐브 $FQ_{2d-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보인다.

• The Transactions of the Korea Information Processing Society
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• v.6 no.7
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• pp.1756-1769
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• 1999

Parallel paths in an interconnection network have some significance in that message transmission time can be reduced because message is divided into packets and transmitted in parallel through several paths, and also an whose nodes has 2n binary bit string, is an interconnection network which has a lower network cost than hypercube and its variation. In this paper, we analyze node disjoint parallel path in Folded Hyper-Star graph FHS(2n,n) proposed as the topology of parallel computers and, using the result, prove that the fault diameter of a Folded Hyper-Star graph FHS(2n,n) is 2n-1.

• The KIPS Transactions:PartA
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• v.9A no.3
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• pp.333-340
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• 2002

Embedding is a mapping an interconnection network G to another interconnection network H. If a network G can be embedded to another network H, algorithms developed on G can be simulated on H. In this paper, we first propose a method to embed between Hierarchical Cubic Network HCN(n, n) and Hierarchical Folded-hypercube Network HFN(n, n). HCN(n, n) and HFN(n, n) are graph topologies having desirable properties of hypercube while improving the network cost, defined as degree${\times}$diameter, of Hypercube. We prove that HCN(n, n) can be embedded into HFN(n, n) with dilation 3 and congestion 2, and the average dilation is less than 2. HFN(n, n) can be embedded into HCN(n, n) with dilation 0 (n), but the average dilation is less than 2. Finally, we analyze the fault tolerance of HCN(n, n) and prove that HCN(n, n) is maximally fault tolerant.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.11a
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• pp.667-670
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• 2007

알고리즘의 설계에 있어서 주어진 연결망을 다른 연결망으로 임베딩하는 것은 알고리즘을 활용하는 중용한 방법중의 하나이다. 본 논문에서는 하이퍼큐브보다 망비용이 개선된 이븐 연결망과 오드 연결망 사이의 임베딩을 분석하고, 이븐 연결망이 이분할 연결망임을 보인다. 이븐 연결망을 오드 연결망에 연장율 2, 밀집율 1에 임베딩 가능함을 보이고, 오드 연결망을 이븐 연결망에 연장율 2, 밀집율 1에 임베딩 가능함을 보인다.