• 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.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1137-1139
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• 1987

We discuss several issues related to the sorting algorithms on hypercube machine. The efficiencies of the algorithms are compared under the simpler assumption and the load balancing problem arising from the various algorithms and the data distribution is also discussed.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.5C
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• pp.320-328
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• 2005

Hypercube has a capability of fault-tolerance and regularity, which is easy to develop an algorithm. Many algorithms have been developed as an efficient fault-tolerance routing algorithm using hypercube. Among these algorithms, a method which use safe and unsafe concept was developed by Masuyama. Masuyama suggested an enhanced algorithm that take advantage of unsafe-safe concept. In this paper, we propose an algorithm that uses the unsafe, safe concept and modify Masuyama's algorithm. Using simulator we compare the performance of the proposed algorithm with existing algorithms.

• 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.

• The KIPS Transactions:PartA
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• v.18A no.6
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• pp.225-232
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• 2011

Restricted Hypercube-Like (RHL) graphs are a graph class that widely includes useful interconnection networks such as crossed cube, Mobius cube, Mcube, twisted cube, locally twisted cube, multiply twisted cube, and generalized twisted cube. In this paper, we show that for an m-dimensional RHL graph G, $m{\geq}4$, with an arbitrary faulty edge set $F{\subset}E(G)$, ${\mid}F{\mid}{\leq}m-2$, graph $G{\setminus}F$ has a hamiltonian path between any distinct two nodes s and t if dist(s, V(F))${\neq}1$ or dist(t, V(F))${\neq}1$. Graph $G{\setminus}F$ is the graph G whose faulty edges are removed. Set V(F) is the end vertex set of the edges in F and dist(v, V(F)) is the minimum distance between vertex v and the vertices in V(F).

• 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.