• Journal of Korea Multimedia Society
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• v.5 no.1
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• pp.114-119
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• 2002

Realtime assignment of railways is an important component in the railway control systems. To solve this problem, we must exactly represent the track topology. Graph is a proper data structure for representing general network topologies, but not Proper for track topologies. In this paper, we define a new data structure, railway graph, which can exactly represent topologies of railway networks. And we describe a path search algorithm in the defined railway graph, and a top-down approach for designing railway network by the Proposed graph.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.2D
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• pp.171-179
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• 2010

The purpose of the present study is to suggest composing the graph topology of sketch drawing element and the recognition of the shape pattern for the earthwork quantity calculation. The algorithm which can extract the topology element such as vertex, edge, face and establish the relation between each topology was developed. The model which can define earthwork graph and recognize the shape pattern of earthwork was presented. As a result of the study, the shape pattern of earthwork that can't be calculated by existing earthwork calculation program could be recognized as expanding this model. The earthwork shape recognition automation using the graph topology model can be applied to the automation for the earthwork quantity estimation.

• 전기의세계
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• v.28 no.3
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• pp.27-34
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• 1979

회로망을 해석하는데는 i) 지로해석법, ii) 루우프해석법, iii) 메슈해석법, iv) 마디해석법, v) 컷세트해석법및 vi) 상태공간해석법 등이 사용됨은 이미 알고 있다. 다루는 회로가 비교적 간단한 구성의 선형, 시불변 회로망이고 또한 종이와 연필로 회로망해석을 수행하여야 될때에는 익혀온 이들 해석법을 관례대로 따르면 될 것이나, 다룰려는 회로망이 대형인 복잡한 구조의 것이든지 혹은 비선형소자, 시변소자 등을 포함하는 경우에는 독립회로방정식들을 체계있게 세워 나가는데에도 어려움이 있거니와, 설혹 회로방정식군을 세웠다 하드라도 이들을 풀어 나가는데에도 이젠 우리가 할 수 있는 능력한계를 느끼게 된다. 전자계산기가 스스로 독립성을 지닌 필요한 개수의 회로망방정식들을 작성하고, 또한 풀이도 요구되는 특성을 갖는 회로망을 설계하여주면, 많은 수고와 번거로움이 덜어진다. 이러한 뜻에서 전산기의 활용에 의한 회로망의 해석, 설계 (computer oriented network analysis and synthesis)이론이 바람직하다. 여기서는 이러한 전산기의 사용에 의한 회로망의 해석, 설계이론의 기초가 되는 부분을 가려서 위상 그래프이론에 따른 회로망 해석방법을 해설한다.

• Proceedings of the Korean Information Science Society Conference
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• 2006.06b
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• pp.232-234
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• 2006

본 논문에서는 마르코프 결정 문제 (Markov decision problem)의 풀이 효율을 잴 수 있는 척도를 알아보기 위해 복잡계 네트워크 (complex network) 의 관점에서 MDP를 하나의 그래프로 나타내고, 그 그래프의 위상학적 성질들을 여러 네트워크 척도 (network measurements)들을 이용하여 측정하고 그 MDP의 풀이 효율과의 관계를 분석하였다. 실세계의 여러 문제들이 MDP로 표현될 수 있고, 모델이 알려진 경우에는 평가치 반복(value iteration)이나 모델이 알려지지 않은 경우에도 강화 학습(reinforcement learning) 알고리즘등을 사용하여 풀 수 있으나, 이들 알고리즘들은 시간 복잡도가 높아 크기가 큰 실세계 문제에 적용하기 쉽지 않다. 이 문제를 해결하기 위해 제안된 것이 MDP를 계층적으로 분할하거나, 여러 단계를 묶어서 수행하는 등의 시간적 추상화(temporal abstraction) 방법들이다. 시간적 추상화를 도입할 경우 MDP가 보다 효율적으로 풀리는 꼴로 바뀐다는 사실에 착안하여, MDP의 풀이 효율을 네트워크 척도를 이용하여 측정할 수 있는 여러 위상학적 성질들을 기반으로 분석하였다. 다양한 구조와 파라미터를 가진 MDP들을 사용해 네트워크 척도들과 MDP의 풀이 효율간의 관계를 분석해 본 결과, 네트워크 척도들 중 평균 측지 거리 (mean geodesic distance) 가 그 MDP의 풀이 효율을 결정하는 가장 중요한 기준이라는 사실을 알 수 있었다.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.1
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• pp.291-299
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• 2016

This paper raises a question of whether a simple periodic phenomenon is associated with the topology and provides the convincing answers to it. A variety of music instrumental sound signals are used to prove our assertion, which are embedded in Euclidean space to analyze their topologies by computing the homology groups. A commute time embedding is employed to transform segments of waveforms into the corresponding geometries, which is implemented by organizing patches according to the graph-based metric. It is shown that commute time embedding generates the intrinsic topological complexities although their geometries are varied according to the spectrums of the signals. This paper employs a persistent homology to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, and discusses their applications.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.5
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• pp.411-419
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• 2013

Research on developing algorithms for building modeling such as extracting outlines of the buildings and segmenting patches of the roofs using aerial images or LiDAR data are active. However, utilizing information from the building model is not well implemented yet. This study aims to propose a scheme for search identical or similar shape of buildings by utilizing graph topology pattern matching under the assumptions: (1) Buildings were modeled beforehand using imagery or LiDAR data, or (2) 3D building data from digital maps are available. Side walls, segmented roofs and footprints were represented as nodes, and relationships among the nodes were defined using graph topology. Topology graph database was generated and pattern matching was performed with buildings of various shapes. The results show that efficiency of the proposed method in terms of reliability of matching and database structure. In addition, flexibility in the search was achieved by altering conditions for the pattern matching. Furthermore, topology graph representation could be used as scale and rotation invariant shape descriptor.

• 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.

• 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.

• Geophysics and Geophysical Exploration
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• v.12 no.1
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• pp.105-113
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• 2009

The interpretation of observed waveform characteristics identified in refraction and wide-angle reflection data increases confidence in the crustal structure model obtained. When calculating traveltimes and raypaths, wavefront methods on a regular grid based on graph theory are robust even with complicated structures, but basically compute only first arrivals. In this paper, we develop new algorithms to compute traveltimes and raypaths not only for first arrivals, but also for fast and later reflection arrivals, later refraction arrivals, and converted waves between P and S, using the modified wavefront method based on slowness network nodes mapped on a multi-layer model. Using the new algorithm, we can interpret reflected arrivals, Pg-later arrivals, strong arrivals appearing behind Pn, triplicated Moho reflected arrivals (PmP) to obtain the shape of the Moho, and phases involving conversion between P and S. Using two models of an ocean-continent transition zone and an oceanic ridge or seamount, we show the usefulness of this algorithm, which is confirmed by synthetic seismograms using the 2D Finite Difference Method (2D-FDM). Characteristics of arrivals and raypaths of the two models differ from each other in that using only first-arrival traveltime data for crustal structure analysis involves risk of erroneous interpretation in the ocean-continent transition zone, or the region around a ridge or seamount.