• 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.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.535-543
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• 1997

The application of Hadamard matrix to the paral-lel routings on the hypercube network was presented by Rabin. In this matrix every two rows differ from each other by exactly n/2 positions. A set of n disjoint paths on n-dimensional hypercube net-work was designed using this peculiar property of Hadamard ma-trix. Then the data is dispersed into n packets and these n packet are transmitted along these n disjoint paths. In this paper Rabin's routing algorithm is analyzed in terms of covering problem and as-signment problem. Finally we conclude that n packets dispersed are placed in well-distributed positions during transmisson and the ran-domly selected paths are almost a set of n edge-disjoint paths with high probability.

• 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).

• The Transactions of the Korea Information Processing Society
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• v.6 no.1
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• pp.75-83
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• 1999

recently, a new hypercube-like interconnection network, the Z-cube, was proposed. The Z-cube retains most good topological properties, however, its node degree is 3/4 of hypercube's one. Considering hardware implementations, the Z-cube is a good alternative to the hypercube. In this paper, we obtained the diameter, fault diameter and the average distance between two nodes to evaluate the communication performance of the Z-cube. The recursive structure, the shortest path between two nodes I Z-cube and recurrence relation on the average distance were deduced, and node disjoint path was introduced. Although it is generally expected that the communication performance in an interconnection network with reduced node degree falls as much as that, this paper shows that the Z-cube's diameter is the same as the hypercube's one and the average distance between two nodes in Z-cube is about 1.125 times the average distance between two nodes in the hypercube and the fault diameter of Z-cube ranges approximately from 1.4times to 1.7times the fault diameter of the hypercube.

• Proceedings of the IEEK Conference
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• 2000.11c
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• pp.59-62
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• 2000

In this paper, We propose the new interconnection network which is designed to edge numbering method using inorder traversal a Fibonacci trees and its jump sequence is Fibonacci numbers. It has a simple (shortest path)routing algorithm, diameter, node degree. It has a spaning subtree which is Fibonacci tree and it is embedded Fibonacci tree. It is compared with Hypercube. We improve diameter compared with Hypercube on interconnection network measrtes.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.3
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• pp.158-170
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• 2009

In this paper, we propose the new torus network which has the hypercube Q3 as the basic module. The proposed Hyper-torus has the degree 4, and is the network which has the scalability, and the fine diameter. If we compare the class of the torus in the viewpoint of network cost, the hyper-torus with $1.4{\sqrt{N}}$+ 16 is proved to be approximately 65% than the torus with $4{\sqrt{N}}$ and 50% than the honeycomb with $2.45{\sqrt{N}}$. This result means that hyper-torus is better for the class of the existing mesh in the viewpoint of network cost.

• 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.

• Annual Conference of KIPS
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• 2000.10a
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• pp.633-636
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• 2000

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

• Journal of Communications and Networks
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• v.14 no.2
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• pp.213-221
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• 2012

The architecture of an interconnection network is usually represented by a graph, and a graph G is bipancyclic if it contains a cycle for every even length from 4 to ${\mid}V(G){\mid}$. In this article, we analyze the conditional edge-fault-tolerant properties of an enhanced hypercube, which is an attractive variant of a hypercube that can be obtained by adding some complementary edges. For any n-dimensional enhanced hypercube with at most (2n-3) faulty edges in which each vertex is incident with at least two fault-free edges, we showed that there exists a fault-free cycle for every even length from 4 to $2^n$ when n($n{\geq}3$) and k have the same parity. We also show that a fault-free cycle for every odd length exists from n-k+2 to $2^n-1$ when n($n{\geq}2$) and k have the different parity.

• Annual Conference of KIPS
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• 2007.05a
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• pp.749-750
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• 2007

본 논문에서는 네트워크 장비를 사용하지 않고 hypercube topology를 기반으로 PC 들을 직접 연결하여 PC 클러스터를 구현하고 그 실용성을 검증한다. Hypercube 방식의 네트워크는 통신 장비를 사용하지 않기 때문에 저렴하고 보다 안정적이며, 네트워크 부하가 적어 높은 성능의 클러스터 시스템을 구축할 수 있는 것으로 알려져 있다. Hypercube 네트워크의 성능을 알아보기 위하여 다양한 성능 분석 툴 및 병렬 프로그램을 통하여 Gigabit 스위치를 사용한 네트워크와 비교/분석 한다.