• The Transactions of the Korea Information Processing Society
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• v.7 no.5
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• pp.1464-1473
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• 2000

In this paper, we analyze the cycle property of the (n,k)-star graph that has an attention as an alternative interconnection network topology in recent years. Based on the graph-theoretic properties in (n,k)-star graphs, we show the pancyclic property of the graph and also present the corresponding algorithm. Based on the recursive structure of the graph, we present such top-down approach that the resulting cycle can be constructed by applying series of "dimension expansion" operations to a kind of cycles consisting of sub-graphs. This processing naturally leads to such property that the resulting cycles tend to be integrated compactly within some minimal subset of sub-graphs, and also means its applicability of another classes of the disjoint-style cycle problems. This result means not only the graph-theoretic contribution of analyzing the pancyclic property in the underlying graph model but also the parallel processing applications such a as message routing or resource allocation and scheduling in the multi-computer system with the corresponding interconnection network.

• The KIPS Transactions:PartA
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• v.13A no.3 s.100
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• pp.253-260
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• 2006

In this paper, we analyze the Hamiltonian property of Pyramid graphs. We prove that it is always possible to construct a Hamiltonian cycle of length $(4^N-1)/3$ by applying the proposed algorithm to construct series of cycle expansion operations into two adjacent cycles in the Pyramid graph of height N.

• Annual Conference of KIPS
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• 2007.11a
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• pp.585-587
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• 2007

본 논문에서는 피라미드 그래프 내에 내재된 사이클 특성을 분석한다. 사이클 확장 연산을 이용하여 사이클의 크기를 신장시켜 나가는 일련의 과정에서 가능한 모든 정점들을 포함시키기 위해 불가피하게 피해야 할 조건들에 대해 분석한다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.10a
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• pp.773-775
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• 2013

In this paper, we consider the problem for finding a vertex sequence of the directed cycle graph from the individual neighborhood information on a reconfigurable mesh(in short, RMESH). This problem can be solved in linear time using a sequential algorithm. However, it is difficult to develop a sublinear time parallel algorithm for the problem because of its sequential nature. All kinds of polygons can be represented by directed cycles, hence a solution of the problem may be used to solving problems in which a polygon should be constructed from the adjacency information for each vertex. In this paper, we present a constant time $n{\times}n^2$ RMESH algorithm for the problem with n vertices.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.2
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• pp.35-42
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• 2014

This paper suggests a method that obtains the minimum spanning tree (MST) far more easily and rapidly than the present ones. The suggested algorithm, firstly, simplifies a graph by means of reducing the number of edges of the graph. To achieve this, it applies a method of eliminating the maximum weight edge if the valency of vertices of the graph is equal to or more than 3. As a result of this step, we can obtain the reduced edge population. Next, it applies a method in which the maximum weight edge is eliminated within the cycle. On applying the suggested population minimizing and maximum weight edge deletion algorithms to 9 various graphs, as many as the number of cycles of the graph is executed and MST is easily obtained. It turns out to lessen 66% of the number of cycles and obtain the MST in at least 2 and at most 8 cycles by only deleting the maximum weight edges.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.6
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• pp.91-97
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• 2022

There is hare and tortoise racing algorithm(HTA) for single-source(SS) singly linked list(SLL) with O(n) time complexity. But the fast method is unknown for general graph with multi-source, multi-destination, and multi-branch(MSMDMB). This paper suggests linear time cycle detection algorithm for given undirected and digraph with MSMDMB. The proposed method reduced the given graph G contained with unnecessary vertices(or nodes) to cycle into reduced graph G' with only necessary vertices(or nodes) to cycle based on the condition of cycle formation. For the reduced graph G', we can be find the cycle set C and cycle length λ using linear search within linear time. As a result of experiment data, the proposed algorithm can be obtained the cycle for whole data.

• The KIPS Transactions:PartA
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• v.15A no.2
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• pp.119-124
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• 2008

In this paper, we analyze a cycle property embedded in pyramid graphs. We prove that it is always possible to construct diverse cycles of all lengths from 3 to ($4^N-1$)/3 by applying series of cycle expansion operations to the pyramid graph of height N. This means that the pyramid graph has the pancyclic property.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.1
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• pp.149-154
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• 2024

This paper proposes an algorithm that remedy Floyd's the tortoise and the hare algorithm (THA) shortcomings which is specialized in singly linked list (SLL), so this algorithm fails to detect the cycle in undirected graph, digraph, and tree with multiple inputs or outputs. The proposed algorithm simply pruning the source and sink with only one edge using cycle detection of single edge node pruning. As a result of the experimental of various list, undirected graph, digraph, and tree, the proposed algorithm can be successively detect the cycle all of them. Thus, the proposed algorithm has the simplest and fastest advantage in the field of cycle detection.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.4
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• pp.233-241
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• 2014

This paper suggests a fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property. Borůvka algorithm firstly gets the partial spanning tree using cycle property for one-edge connected graph that selects the only one minimum weighted edge (e) per vertex (v). Additionally, that selects minimum weighted edge between partial spanning trees using cut property. Kruskal algorithm uses cut property for ascending ordered of all edges. Reverse-delete algorithm uses cycle property for descending ordered of all edges. Borůvka and Kruskal algorithms always perform |e| times for all edges. The proposed algorithm obtains 2-edge connected graph that selects 2 minimum weighted edges for each vertex firstly. Secondly, we use cycle property for 2-edges connected graph, and stop the algorithm until |e|=|v|-1 For actual 10 benchmark data, The proposed algorithm can be get the minimum spanning trees. Also, this algorithm reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.

• Annual Conference of KIPS
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• 2005.11a
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• pp.867-870
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• 2005

본 논문에서는 피라미드 그래프를 대상으로 링을 임베딩하는 문제를 다룬다. 사이클 확장 연산을 이용하는 사이클의 크기를 확대시켜 나가는 일련의 과정을 통하여 최대 크기의 링을 의미하는 헤밀톤 사이클을 찾을 수 있는 알고리즘을 제시함으로써 임의의 높이 N인 피라미드 그래프 내에 길이 $4^N-1/3$인 링을 임베딩 할 수 있음을 증명한다.