• Journal of Korea Multimedia Society
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• v.9 no.9
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• pp.1173-1183
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• 2006

Matrix-star, Pancake, and RFM graphs have such a good property of Star graph and a lower network cost than Hypercube. Matrix-star graph has Star graph as a basic module and the node symmetry, the maximum fault tolerance, and the hierarchical decomposition property. Also it is an interconnection network that improves the network cost against Star graph. In this paper, we propose a method to embed among Matrix-star Pancake, and RFM graphs using the edge definition of graphs. We prove that Matrix-star $MS_{2,n}$ can be embedded into Pancake $P_{2n}$ with dilation 4, expansion 1, and $RFM_{n}$ graphs can be embedded into Pancake $P_{n}$ with dilation 2. Also, we show that Matrix-star $MS_{2,n}$ can be embedded into the $RFM_{2n}$ with average dilation 3.

• Journal of Korea Multimedia Society
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• v.6 no.3
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• pp.556-564
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• 2003

A Star and Pancake graph also have such a good property of a hypercube and have a low network cost than the hypercube. A Macro-star graph which has the star graph as a basic module has the node symmetry, the maximum fault tolerance, and the hierarchical decomposition property. And, it is an interconnection network which improves the network cost against the Star graph. In this paper, we propose a method to embed between Star graph, Pancake graph, and Macro-star graph using the edge definition of graphs. We prove that the Star graph $S_n$ can be embedded into Pancake graph $P_n$ with dilation 4, and Macro-star graph MS(2,n) can be embedded into Pancake graph $P_{2n＋1}$ with dilation 4. Also, we have a result that the embedding cost, a Pancake graph can be embedded into Star and Macro-star graph, is O(n).

• The Journal of the Korea Contents Association
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• v.9 no.12
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• pp.582-591
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• 2009

The pyramid graph is an interconnection network topology based on regular square mesh and tree structures. In this paper, we adopt a strategy of classification into two disjoint groups of edges in regular square mesh as a base sub-graph constituting of each layer in the pyramid graph. Edge set in the mesh can be divided into two disjoint sub-sets called as NPC(represents candidate edge for neighbor-parent) and SPC(represents candidate edge for shared-parent) whether the parents vertices adjacent to two end vertices of the corresponding edge have a relation of neighbor or shared in the upper layer of pyramid graph. In addition, we also introduce a notion of shrink graph to focus only on the NPC-edges by hiding SPC-edges in the original graph within the shrunk super-vertex on the resulting graph. In this paper, we analyze that the lower and upper bound on the number of NPC-edges in a Hamiltonian cycle constructed on $2^n\times2^n$ mesh is $2^{2n-2}$ and $3*(2^{2n-2}-2^{n-1})$ respectively. By expanding this result into the pyramid graph, we also prove that the maximum number of NPC-edges containable in a Hamiltonian cycle is $4^{n-1}-3*2^{n-1}$-2n+7 in the n-dimensional pyramid.

• The KIPS Transactions:PartA
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• v.15A no.6
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• pp.345-350
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• 2008

Recently, a HyperStar network HS(2n,n) has been introduced as a new interconnection network of new topology for parallel processing. HyperStar network 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 a construction algorithm of edge-disjoint spanning trees in HyperStar network HS(2n,n). Also, we prove that edge-disjoint spanning tree by the algorithm is optimal.

• The Journal of the Korea institute of electronic communication sciences
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• v.5 no.5
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• pp.444-448
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• 2010

RCR network[1] is a topology for interconnection networks having many desirable properties for building scalable parallel machines. This had been analyzed by Hu and Cao[2] to deal with problems of disconnected graph, bisection width and diameter. We analyze some properties of RCR again and revise the condition for connected graph and network diameter. And we present an efficient algorithm for finding next node on a shortest path.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.11B
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• pp.946-955
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• 2004

It is shown that the do Bruijn graph (dBG) can be used as an architecture for interconnection network and a suitable structure for parallel computation. Recent works have classified dBG based routing algorithms into shortest path routing and fault tolerant routing but investigation into fault free shortest path (FFSP) on dBG has been non-existent. In addition, as the size of the network increase, more faults are to be expected and therefore shortest path dBG algorithms in fault free mode may not be suitable routing algorithms for real interconnection networks, which contain several failures. Furthermore, long fault free path may lead to high traffic, high delay time and low throughput. In this paper we investigate routing algorithms in the condition of existing failure, based on the Bidirectional do Bruijn graph (BdBG). Two FFSP routing algorithms are proposed. Then, the performances of the two algorithms are analyzed in terms of mean path lengths and discrete set mean sizes. Our study shows that the proposed algorithms can be one of the candidates for routing in real interconnection networks based on dBG.

• 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)

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.999-1007
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k )를 그래프 이론적 관점에서 고찰하고 정점이 서로소인 사이클과 그래프 invariant에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )가 길이 사이클을 가질 필요 충분 조건을 구하고, 이 조건하에서 G(2^m , 2^k )는 가능한 최대 개수의 정점이 서로소이고 길이가l`인 사이클을 가짐을 보인다. 그리고 정점 및 에지 채색, 최대 클릭, 독립 집합 및 정점 커버에 대한 그래프 invariant를 분석한다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties of G(2^m , 2^k ) concerned with vertex-disjoint cycles and graph invariants. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . A necessary and sufficient condition for recursive circulant {{{{G(2^m , 2^k ) to have a cycle of lengthl` is derived. Under the condition, we show that G(2^m , 2^k ) has the maximum possible number of vertex-disjoint cycles of length l`. We analyze graph invariants on vertex and edge coloring, maximum clique, independent set and vertex cover.

• The KIPS Transactions:PartA
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• v.17A no.1
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• pp.1-8
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• 2010

The fault diameter is one of the important measures for transmission rate and reliability of interconnection network. H.-O. Lee et al.[Parallel paths in folded hyper-star graph, Journal of KIPS, Vol.6, No.7, pp.1756-1769, 1999] suggested the node-disjoint paths of FHS (2n,n), and proved that the fault diameter of FHS(2n,n) is less than 2n-1. In this paper, we suggest an advanced node-disjoint paths of FHS(2n,n). We also prove that the wide diameter of FHS(2n,n) is dist(U,V)+4, and the fault diameter of FHS(2n,n) is less than n+2.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.7
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• pp.117-124
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• 1994

In this pape, we propose a graph-theoretic approach for solving the allocation problem for the synthesis of datapaths based on multiport memories. An efficient algorithm is devised by using the weighted bipartite matching algorithm to assign variables to each port of memory modules. The proposed algorithm assigns program variables into a minimum number of multiport memory modules such that usage of memory elements and interconnection cost can be kept minimal. Experimental results show that the proposed algorithm generates the datapaths with fewer registers in memory modules and less interconnection cost for several benchmarks available from the literatures.