• 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 Korea Multimedia Society
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• v.13 no.8
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• pp.1183-1193
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• 2010

The pyramid graph is well known in parallel processing as a interconnection network topology based on regular square mesh and tree architectures. The enhanced pyramid graph is an alternative architecture by exchanging mesh into the corresponding torus on the base for upgrading performance than the pyramid. In this paper, we adopt a strategy of classification into two disjoint groups of edges in regular square torus as a basic sub-graph constituting of each layer in the enhanced pyramid graph. Edge set in the torus graph is considered as two disjoint sub-sets called 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 sharing in the upper layer of the enhanced pyramid graph. In addition, we also introduce a notion of shrink graph to focus only on the NPC-edges by hiding SPC-edges within the shrunk super-vertex on the resulting shrink graph. In this paper, we analyze that the lower and upper bounds on the number of NPC-edges in a Hamiltonian cycle constructed on $2^n{\times}2^n$ torus is $2^{2n-2}$ and $3{\cdot}2^{2n-2}$ respectively. By expanding this result into the enhanced pyramid graph, we also prove that the maximum number of NPC-edges containable in a Hamiltonian cycle is $4^{n-1}$-2n+1 in the n-dimensional enhanced pyramid.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.3
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• pp.313-323
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• 2000

In this paper, we consider ring embedding problem on (n,k)-star graphs. We first present a new ring embedding strategy and also prove the superiority in expandability by showing its application into the fault-tolerant ring embedding problem with edge faults. This result can be applied to the multicating applications that use the underlying cycle properties on the multi-computer system.

• Annual Conference of KIPS
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• 2009.04a
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• pp.981-983
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• 2009

피라미드 그래프는 정방형 메쉬와 트리 구조를 기반으로 하는 상호연결망 토폴로지다. 정방형 메쉬 내에서 NPC-간선은 해당 메쉬를 피라미드의 부그래프 관점에서 해석할 때 NPC-간선의 양 끝 노드들의 부모 노드들이 상위 계층의 메쉬 부그래프 내에서 서로 인접하게 되는 간선으로써 사이클 확장이나 고장허용 특성의 관점에서 중요한 의미를 갖는 간선이다. 본 연구에서는 $2^n{\times}2^n$ 2-차원 정방형 메쉬 내에서 헤밀톤 사이클 구성 시 포함할 수 있는 NPC-간선 개수의 하한값이 $2^{2n-2}$임을 분석한다.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04a
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• pp.742-744
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• 2001

이 논문은 n-차원 스타 그래프 S$_{n}$, n$\geq$4에서 정점과 에지 고장의 수가 n-3 이하일 때, 임의의 두 고장이 아닌 정점 사이에 길이가 두 정점의 색이 같으면 n!-2f$_{v}$ -2 이상이고, 색이 다르면 n!-2f$_{v}$ -1 이상인 경로가 존재함을 보인다. 여기서 f$_{v}$ 는 고장인 정점의 수이다. 이 결과를 이용하면 고장의 수가 n-3이하일 때, 임의의 고장이 아닌 에지를 지나는 길이 n!-2f$_{v}$ 이상인 사이클을 설계할 수 있다.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.1
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• pp.22-34
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• 2002

In this paper, we consider ring embeding problem in faulty (n,k) star graphs which is recently proposed as an alternative interconnection network topology, By effectively utilizing such strategies as series of dimension expansions and even distribution of faulty nodes into sub-stars in graph itself. we prove that it is possible to construct a maximal fault-free ring excluding only faulty nodes when the number of faults is no more than n-3 and $n-k{\geq}2$, and also propose an algorithm which can embed the corresponding ring in (n.k)-star graphs This results will be applied into the multicasting applications that the underlying cycle properties on the multi-computer system.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.1_2
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• pp.86-94
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• 2004

In this paper, we show that $ G(2^m, 4), m{\geq}3$with at most m-2 faulty elements has a fault-free cycle of length 1 for every ${\leq}1{\leq}2^m-f_v$ is the number of faulty vertices. To achieve our purpose, we define a graph G to be k-fault hypohamiltonian-connected if for any set F of faulty elements, G- F has a fault-free path joining every pair of fault-free vertices whose length is shorter than a hamiltonian path by one, and then show that$ G(2^m, 4), m{\geq}3$ is m-3-fault hypohamiltonian-connected.

• 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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.31 no.3
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• pp.24-34
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• 2008

본 논문은 존 조정하에서의 자동반송차량 네트워크에서 발생하는 고착을 해결하기 위한 두 가지 효과적인 알고리듬을 소개한다. 이 알고리듬들은 특별히 양방향 네트워크에 알맞도록 고안되었다. 사이클 제거 알고리듬은 고착을 예방하기 위한 차량의 안전한 라우트를 결정하나, 그래프 축소 알고리듬은 고착을 회피하기 위하여 미래 잠재적인 고착 발생 조건을 결정한다. 시뮬레이션을 통하여 알고리듬들의 성능을 비교 분석한 결과 작업물의 이동 횟수와 알고리듬의 시간 복잡성 측면에서 그래프 축소 알고리듬이 사이클 제거 알고리듬 보다 우수함을 나타내었다.

• Journal of the Korea Society of Computer and Information
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• v.20 no.3
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• pp.107-113
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• 2015

This paper presents a polynomial time algorithm to the minimum cardinality feedback edge set and minimum weight feedback edge set problems. The algorithm makes use of the property wherein the sum of the minimum spanning tree edge set and the minimum feedback edge set equals a given graph's edge set. In other words, the minimum feedback edge set is inherently a complementary set of the former. The proposed algorithm, in pursuit of the optimal solution, modifies the minimum spanning tree finding Kruskal's algorithm so as to arrange the weight of edges in a descending order and to assign cycle-deficient edges to the maximum spanning tree edge set MXST and cycle-containing edges to the feedback edge set FES. This algorithm runs with linear time complexity, whose execution time corresponds to the number of edges of the graph. When extensively tested on various undirected graphs both with and without the weighed edge, the proposed algorithm has obtained the optimal solutions with 100% success and accuracy.