• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.2
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• pp.429-434
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• 2017

In a graph G=(V, E) with n vertices, there is an unique box which is finally laid on each vertex. Thus each vertex and box is both numbered from 1 to n and the box i should be laid on the vertex i. But, the box ${\pi}$(i) is initially located on the vertex i according to a permutation ${\pi}$. In each step, the robot can walk along an edge of G and can carry at most one box at a time. Also when arriving at a vertex, the robot can swap the box placed there with the box it is carrying. The problem is to minimize the total step so that every vertex has its own box, that is, the shuffled boxes are sorted. In this paper, we shall find an upper bound of the minimum number of steps and show that the movement of the robot is found in $O(n^2)$ time when G is a cycle.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.1
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• pp.37-42
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• 2024

This paper suggests polynomial time algorithm for cutwidth minimization problem that classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. To find the minimum cutwidth CW_f(G)=max_𝜈∈_VCW_f(𝜈)for given graph G=(V,E),m=｜V｜, n=｜E｜, the proposed algorithm divides neighborhood N_G[𝜈_i] of the maximum degree vertex 𝜈_i in graph G into left and right and decides the vertical cut plane with minimum number of edges pass through the vertex 𝜈_i firstly. Then, we split the left and right N_G[𝜈_i] into horizontal sections with minimum pass through edges. Secondly, the inner-section vertices are connected into line graph and the inter-section lines are connected by one line layout. Finally, we perform the optimization process in order to obtain the minimum cutwidth using vertex moving method. Though the proposed algorithm requires O(n²) time complexity, that can be obtains the optimal solutions for all of various experimental data

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• The Journal of the Korea Contents Association
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• v.18 no.3
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• pp.70-80
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• 2018

Due to the recent development of social media and mobile devices, graph data have been using in various fields. In addition, caching techniques for reducing I/O costs in the process of large capacity graph data have been studied. In this paper, we propose a multi-layer caching scheme considering the connectivity of the graph, which is the characteristics of the graph topology, and the history of the past subgraph usage. The proposed scheme divides a cache into Used Data Cache and Prefetched Cache. The Used Data Cache maintains data by weights according to the frequently used sub-graph patterns. The Prefetched Cache maintains the neighbor data of the recently used data that are not used. In order to extract the graph patterns, their past history information is used. Since the frequently used sub-graphs have high probabilities to be reused, they are cached. It uses a strategy to replace new data with less likely data to be used if the memory is full. Through the performance evaluation, we prove that the proposed caching scheme is superior to the existing cache management scheme.

• Journal of Life Science
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• v.18 no.4
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• pp.565-571
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• 2008

Due to rapid development of bioinformatics technologies, various biological data have been produced in silico. So now days complicated and large scale biodata are used to accomplish requirement of researcher. Developing visualization and annotation tool using them is still hot issues although those have been studied for a decade. However, diversity and various requirements of users make us hard to develop general purpose tool. In this paper, I propose a novel system, Genome Viewer and Annotation tool (GenoVA), to annotate and visualize among genomes using known information and multiple relation graph. There are several multiple alignment tools but they lose conserved area for complexity of its constrains. The GenoVA extracts all associated information between all pair genomes by extending pairwise alignment. High frequency conserved area and high BLAST score make a block node of relation graph. To represent multiple relation graph, the system connects among associated block nodes. Also the system shows the known information, COG, gene and hierarchical path of block node. In this case, the system can annotates missed area and unknown gene by navigating the special block node's clustering. I experimented ten bacteria genomes for extracting the feature to visualize and annotate among them. GenoVA also supports simple and rough computational annotation of new genome.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.49-56
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• 2012

In this paper we introduce two new labelings called product antimagic labeling and total product antimagic labeling for directed graphs and show the existence of the same for Cayley digraphs of 2-generated 2-groups.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.113-125
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• 2019

In this paper, we introduce the elimination ideal $I_D(G)$ associated to a simple finite graph G. We obtain the upper bound of Castelnuovo-Mumford regularity of elimination ideal for various classes of graphs.

• Proceedings of the Korea Information Processing Society Conference
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• 2023.11a
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• pp.589-591
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• 2023

현재 수치예보 시스템은 항공기, 위성 등 다양한 센서에서 얻은 다종 관측 데이터를 동화하여 대기 상태를 추정하고 있지만, 관측변수 또는 물리량이 서로 다른 관측들을 처리하기 위한 계산 복잡도가 매우 높다. 본 연구에서 기존 시스템의 계산 효율성을 개선하여 관측을 평가하거나 전처리하는 데에 효율적으로 활용하기 위해, 각 관측의 특성을 고려한 자기 지도학습 방법을 통해 멀티모달 기상관측으로부터 실제 대기 상태를 추정하는 방법론을 제안하고자 한다. 비균질적으로 수집되는 멀티모달 기상관측 데이터를 융합하기 위해, (i) 기상관측의 heterogeneous network를 구축하여 개별 관측의 위상정보를 표현하고, (ii) pretext task 기반의 self-supervised learning을 바탕으로 개별 관측의 특성을 표현한다. (iii) Graph neural network 기반의 예측 모델을 통해 실제에 가까운 대기 상태를 추정한다. 제안하는 모델은 대규모 수치 시뮬레이션 시스템으로 수행되는 기존 기술의 한계점을 개선함으로써, 이상 관측 탐지, 관측의 편차 보정, 관측영향 평가 등 관측 전처리 기술로 활용할 수 있다.

• Journal of Internet Computing and Services
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• v.10 no.3
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• pp.131-140
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• 2009

Recently, the information visualization research community has given significant attention to graph visualization, especially visualization of social networks. However, visualization of information flows in a very large social network has not been studied in depth. However, information flows are tightly related to the structure of social networks and it shows dynamic behavior of interactions between members of social networks. Thus, we can get much useful information about social networks from information flows. In this paper, we present our research result that enables users to navigate a very large social network in Google Maps' method and to take a look at information flows on the network. To this end, we devise three techniques; (i) mapping a very large social network to a 2-dimensional graph layout, (ii) exploring the graph to all directions with zooming it in/out, and (iii) building an efficient query processing framework. With these methods, we can visualize very large social networks and information flows in a limited display area with a limited computing resources.

• Spatial Information Research
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• v.14 no.4 s.39
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• pp.391-401
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• 2006

We propose a method for geographically enhanced representation of social networks and implement a Web-based 3D visualization of geographical contexts in social networks. A renovated social network graph is illustrated by using two key components: (i) GWCMs (geographically weighted centrality measures) that reflect the differences in interaction intensity and spatial proximity among nodes and (ii) MSNG (map-integrated social network graph) that incorporates the GWCMs and the geographically referenced arrangement of nodes on a choroplethic map. For the integrated 3D visualization of the renovated social network graph, we employ X3D (Extensible 3D), a standard 3D authoring tool for the Web. An experimental case study of regional R&D collaboration provides a visual clue to geographical contexts in social networks including how the social centralization relates to spatial centralization.