• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.6
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• pp.1361-1368
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• 2014

In this paper, we analyze emddings among HFCube(n,n), HCN(n,n), HFN(n,n) with lower network cost than that of Hypercube. The results are as follows. We propose that $Q_{2n}$ can be embedded into HFCube(n,n) with dilation 5, congestion 2. HCN(n,n) and HFN(n,n) are subgraphs of HFCube(n,n). HFCube(n,n) can be embedded into HFN(n,n) with dilation 3. HFCube(n,n) can be embedded into HCN(n,n) with dilation O(n). The results will be helpful to analyze several efficient properties in each interconnection network.

• School Mathematics
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• v.18 no.2
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• pp.323-348
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• 2016

The 2009 revised national mathematics curriculum have inserted mathematical 'linking cube' activities in the 6th grade math classes to improve students' spatial problem solving abilities and communication skills. However, we found that it was hard for teachers to teach problem solving and communication skills due to the absence of mathematical way of representing linking cubes in the classroom. In this paper, we propose 3D 'turtle representation system' as teaching and learning tools for linking cube activities. After using turtle representation system for linking cube activities, teachers responded that turtle representation system is a valuable problem solving and communication tools for the linking cube mathematics classes. We conclude that turtle representation system is a well designed teaching and learning tools for linking cube activities, and there are lots of educational meanings in the 3D turtle representation system.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.9
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• pp.493-502
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• 2002

The connectivity and edge-connectivity have been the prime deterministic measure of fault tolerance in multicomputer networks. These parameters have a problem that they do not differentiate the different types of disconnected graphs which result from removing the disconnecting vertices or disconnecting edges. To compensate for this shortcoming, one can utilize generalized measures of connectedness such as superconnectivity, toughness, scattering number, vertex-integrity, binding number, and restricted connectivity. In this paper, we analyze such deterministic measures of fault tolerance in recursive circulants and hypercubes, and compare them in terms of fault tolerance.

• Proceedings of the Korean Society of Computer Information Conference
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• 2014.01a
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• pp.77-79
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• 2014

본 논문에서는 Arduino의 I2C 통신을 통해 인터랙티브한 악기를 제안한다. 각각의 큐브는 서로를 인식하고 인식 후 집단이 된 큐브들은 하나의 악기가 된다. Arduino의 통신 핀을 알루미늄 호일에 연결하여 다른 큐브와 접촉 시 통신이 될 수 있도록 하였다. 통신이 이룬 큐브들을 rgbLED 색상 변화를 통해 시각적으로 접촉/비접촉을 나타냈다. 또한 Processing을 통해 그룹이 된 큐브들의 악기 소리를 제어하였다.

• The Transactions of the Korea Information Processing Society
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• v.4 no.8
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• pp.1930-1939
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• 1997

In this paper, we analyze the fault diameter and fault tolerance of Gray cube proposed recently in [12]. fault diameter of an interconnection network is one of the important network measures concerning the distance between nodes when some nodes fail. It is showed that fault diameter of n-dimensional Gray cube having $2^n$ nodes is [(n+1)/2]+2, ($n{\ge}3$). It means the increment of the longest distance between nodes under node-failure is only constant factor. Comparing the result with the fault diameter of well-known hypercube, the longest routing distance of a message in a Gray cube under node-failure is about the half of that hypercube.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.10
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• pp.789-796
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• 2006

An unpaired many-to-many k-disjoint nth cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct sources and sinks in which each vertex of G is covered by a path. Here, a source can be freely matched to a sink. In this paper, we investigate unpaired many-to-many DPC's in a subclass of hpercube-like interconnection networks, called restricted HL-graphs, and show that every n-dimensional restricted HL-graph, $(m{\geq}3)$, with f or less faulty elements (vertices and/or edges) has an unpaired many-to-many k-DPC for any $f{\geq}0\;and\;k{\geq}1\;with\;f+k{\leq}m-2$.

• 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.

• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.249-254
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• 2007

In this paper, we consider the embedding problem of postorder Fibonacci circulant. We show that Fibonacci linear array, Fibonacci mesh, Fibonacci tree, Fibonacci cubes and Hypercube are a subgraph of postorder Fibonacci circulant.

• Proceedings of the IEEK Conference
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• 2003.07d
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• pp.1573-1576
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• 2003

스타 그래프와 팬케익 그래프는 하이퍼큐브가 갖는 좋은 성질을 가지면서 하이퍼큐브보다 망 비용이 적은 값을 갖는 상호연결망이다. 본 논문에서는 그래프의 에지 정의를 이용하여 스타 그래프 S/sub n/은 팬케익 그래프 P/sub n/에 연장율 4, 확장율 1에 임베딩 가능함을 보인다.

• Journal of KIISE:Computer Systems and Theory
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• v.37 no.2
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• pp.61-65
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• 2010

The twisted cube has received great attention because it has several superior properties to the hypercube that is widely known as a versatile parallel processing system. In this paper, we show that node-disjoint $2^{n-1}$ meshes of size $2^n{\times}2^m$ can be embedded into a twisted cube with dilation 1 where $1{\leq}n{\leq}m$. The expansion is 1 for even m and 2 for odd m.