• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.8
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• pp.393-398
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• 2005

In interconnection networks, a Hamiltonian path has been utilized in many applications such as the implementation of linear array and multicasting. In this paper, we consider the Hamiltonian properties of mesh networks which are used as the topology of parallel machines. If a network is strongly Hamiltonian laceable, the network has the longest path joining arbitrary two nodes. We show that a two-dimensional mesh M(m, n) is strongly Hamiltonian laceabie, if $m{\geq}4,\;n{\geq}4(m{\geq}3,\;n{\geq}3\;respectively)$, and the number of nodes is even(odd respectively). A mesh is a spanning subgraph of many interconnection networks such as tori, hypercubes, k-ary n-cubes, and recursive circulants. Thus, our result can be applied to discover the fault-hamiltonicity of such networks.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.8
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• pp.1009-1023
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• 1999

이 논문은 재귀원형군 G(2^m , 2^k ) 그래프 이론적 관점에서 고찰하고 정점이 서로소인 경로에 관한 위상 특성을 제시한다. 재귀원형군은 1 에서 제안된 다중 컴퓨터의 연결망 구조이다. 재귀원형군 {{{{G(2^m , 2^k )의 서로 다른 두 노드 v와 w를 잇는 연결도 kappa(G)개의 서로소인 경로의 길이가 두 노드 사이의 거리d(v,w)나 혹은 G(2^m , 2^k )의 지름 \dia(G)에 비해서 얼마나 늘어나는지를 고려한다. 서로소인 경로를 재귀적으로 설계하는데, 그 길이는 k ge2일 때 d(v,w)+2^k-1과 \dia(G)+2^k-1의 최솟값 이하이고, k=1일 때 d(v,w)+3과 \dia(G)\+2의 최솟값 이하이다. 이 연구는 (2^m , 2^k )의 고장 감내 라우팅, 고장 지름이나 persistence의 분석에 이용할 수 있다.Abstract In this paper, we investigate recursive circulant G(2^m , 2^k ) from the graph theory point of view and present topological properties concerned with node-disjoint paths. Recursive circulant is an interconnection structure for multicomputer networks proposed in 1 . We consider the length increments of {{{{kappa(G)disjoint paths joining arbitrary two nodes v and win G(2^m , 2^k )compared with distance d(v,w)between the two nodes and diameter {{{{\dia(G)of G(2^m , 2^k ), where kappa(G)is the connectivity of G(2^m , 2^k ). We recursively construct disjoint paths of length less than or equal to the minimum of {{{{d(v,w)+2^k-1and \dia(G)+2^k-1for kge2 and the minimum of d(v,w)+3 and \dia(G)+2for k=1. This work can be applied to fault-tolerant routing and analysis of fault diameter and persistence of G(2^m , 2^k )

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.2B
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• pp.325-333
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• 2010

Most communication systems including Wibro use quasi-cyclic LDPC codes composed of circulants. However, it is very difficult to design quasi-cyclic(QC) LDPC codes with optimal degree distribution satisfying conditions on layered decoding and girth due to the restriction of the size of its base matrix. In this paper, we propose a good solution by introducing superposition matrices to QC LDPC codes. We derive the conditions on checking girth of QC LDPC codes with superposition matrices, and propose new decoder to support layered decoding both for original QC LDPC codes and their modifications with superposition matrices. Simulation results show considerable improvements to convergence speed and error-correcting performance of proposed scheme which adopts QC LDPC codes with superposition matrices.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.12
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• pp.665-679
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• 2002

The fault diameter of a graph G is the maximum of lengths of the shortest paths between all two vertices when there are $\chi$(G) - 1 or less faulty vertices, where $\chi$(G) is connectivity of G. In this paper, we analyze the fault diameter of recursive circulant $G(2^m,2^k)$ with $k{\geq}3$. Let $ dia_{m.k}$ denote the diameter of $G(2^m,2^k)$. We show that if $2{\leq}m,2{\leq}k, the fault diameter of $G(2{\leq}m,2{\leq}k)$ is equal to $2^m-2$, and if m=k+1, it is equal to $2^k-1$. It is also shown that for m>k+1, the fault diameter is equal to di a_$m{\neq}1$(mod 2k); otherwise, it is less than or equal to$dia_{m.k+2}$.