• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.293-296
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• 1998

In this paper, we propose a matrix hypercube graph as a new topology for parallel computer and analyze its characteristics of the network parameters, such as degree, routing and diameter. N-dimensional matrix hypercube graph MH(2,n) contains 22n vertices and has relatively lower degree and smaller diameter than well-known hypercube graph. The matrix hypercube graph MH(2,n) and the hypercube graph Q2n have the same number of vertices. In terms of the network cost, defined as the product of the degree and diameter, the former has n2 while the latter has 4n2. In other words, it means that matrix hypercube graph MH(2,n) is better than hypercube graph Q2n with respect to the network cost.

• 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.

• ETRI Journal
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• v.30 no.3
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• pp.483-485
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• 2008

A micro-sensor network is comprised of a large number of small sensors with limited memory capacity. Current key-establishment schemes for symmetric encryption require too much memory for micro-sensor networks on a large scale. In this paper, we propose a memory-efficient hypercube key establishment scheme that only requires logarithmic memory overhead.

• The Transactions of the Korea Information Processing Society
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• v.1 no.1
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• pp.92-98
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• 1994

The hypercube-like interconncetion network,X-hypercubes,has the same number of nodes and edges as conventional hypercubes.By slightly changing the interconneton way between nodes,however,X-hypercubes reduces the diameter by almost half.Thus the communication delay in X-hypercubes can be expected to be much lower than that in hypercubes. This paper gives a new definition of X-hypercubes establishing clear-cut condition of connection between two nodes.As appliction examples of the new definition,this paper presents simple embeddings of hypercubes in X-hypercubes and vice versa.This means that any programs written for hypercubes can be transported onto X-hypercubes and vice versa with minimal overhead.This paper also present bitonic merge sort for X-hypercubes by simulation that for hypercubes.

• The KIPS Transactions:PartA
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• v.9A no.2
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• pp.191-196
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• 2002

It is one of the important measures in the area of algorithm design that any interconnection network should be embedded into another interconnection network for the practical use of algorithm. A HCN(n, n), HFN(n, n) graph also has such a good properties of a hypercube and has a lower network cost than a hypercube. In this paper, we propose a method to embed between hypercube $Q_2n$ and HCN(n, n), HFN(n, n) graph. We show that hypercube $Q_2n$ can be embedded into an HCN(n, n) and KFN(n, n) with dilation 3, and average dilation is smaller than 2. Also, we has a result that the embedding cost, a HCN(n, n) and KFN(n, n) can be embedded into a hypercube, is O(n)

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.5
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• pp.1180-1192
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• 1996

On demand of many users, basic networks of a parallel computer system are required to have a property that can embed various topologies. Bisectional interconnection network is known to satisfy this property, and it can embed various topologies optimally. Nowadays one is very interested in the hypercube as a message pssing multicomputer system, so it is very important to implement a hypercube in bisectional network. In this paper, a hypercube is implemented in a versatile bisecional netork, and its routing and broadcasting algorithm are proposed. Conventional bisectional network can accomodata linear array, complete binary tree and mesh structure as its topology. Now hypercube is implemented to be utilized as a general purpose supercomputercommunication architecture. The proposed routing and broadcasting algorithm embedded in bisectional network are general purpose algorithms which satisfy property of conventional hypercube.

• Journal of Korea Multimedia Society
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• v.3 no.6
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• pp.674-684
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• 2000

One key obstacle which has been identified in achieving parallel processing is to communicate effectively between processors during execution. One approach to achieving an optimal delay time is to use expander graph. The networks and algorithms which are based on expander graphs are successfully exploited to yield fast parallel algorithms and efficient design. The AKS sorting algorithm in time O(logN) which is an important result is based on the use of expanders. The expander graph also can be applied to construct a concentrator and a superconcentrator. Since Margulis found a way to construct an explicit linear expander graph, several expander graphs have been developed. But the proof of existence of such graphs is in fact provided by a nonconstructive argument. We investigate the expander network on the hypercube network. We prove the expansion of a sin81e stage hypercube network and extend this from a single stage to multistage networks. The results in this paper provide a theoretical analysis of expansion in the hypercube network.

• Proceedings of the IEEK Conference
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• 2001.06c
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• pp.63-66
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• 2001

In this paper, We propose the new interconnection network which is designed to edge numbering labeling using postorder traversal which can reduce diameter when it has same node number with Hypercube, which can reduce total node numbers considering node degree and diameter on Fibonacci trees and its jump sequence of circulant is Fibonacci numbers. It has a simple (shortest oath)routing algorithm, diameter, node degree. It has a spaning subtree which is Fibonacci tree and it is embedded to Fibonacci tree. It is compared with Hypercube. We improve diameter compared with Hypercube.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.475-478
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• 1998

The matrix hypercube MH(2,n) is the interconnection network which improves the network cost of the hypercube. In this paper, we propose an algorithm for one-to-all broadcasting in the matrix hypercube MH(2,n). The algorithm can broadcast a message to 22n nodes in O(n) time. The algorithm uses the rich structure of the matrix hypercubes and works by recursively partitioning the original matrix hypercubes into smaller matrix hypercubes.

• The KIPS Transactions:PartA
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• v.11A no.5
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• pp.341-346
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• 2004

Recently A Hyper-Star Graph HS(m, k) has been introduced as a new interconnection network of new topology for parallel processing. Hyper-Star Graph has properties of hypercube and star graph, further improve the network cost of a hypercube with the same number of nodes. In this paper, we show that Hyper-Star Graph HS(m, k) is subgraph of hypercube. And we also show that regular graph, Hyper-Star Graph HS(2n, n) is node-symmetric by introduced mapping algorithm. In addition, we introduce an efficient one-to-all broadcasting scheme - takes 2n-1 times - in Hyper-Star Graph HS(2n, n) based on a spanning tree with minimum height.