• The Journal of the Korea Contents Association
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• v.18 no.2
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• pp.438-449
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• 2018

Recently, various graph data have been utilized in various fields such as social networks and citation networks. As the graph changes dynamically over time, it is necessary to manage the graph historical data for tracking changes and retrieving point-in-time graphs. Most historical data changes partially according to time, so unchanged data is stored redundantly when data is stored in units of time. In this paper, we propose a graph history storage management method to minimize the redundant storage of time graphs. The proposed method continuously detects the change of the graph and stores the overlapping subgraph in intersection snapshot. Intersection snapshots are connected by a number of delta snapshots to maintain change data over time. It improves space efficiency by collectively managing overlapping data stored in intersection snapshots. We also linked intersection snapshots and delta snapshots to retrieval the graph at that point in time. Various performance evaluations are performed to show the superiority of the proposed scheme.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.103-110
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• 2005

This paper is aimed at studying a historical background of graph theory and we deal with the computer representation of graph through a simple example. Graph is represented by adjacency matrix, edge table, adjacency lists and we study the matrix representation by Euler circuit. The effect of the matrix representation by Euler circuit economize the storage capacity of computer. The economy of a storage capacity has meaning on a mobile system.

• The Journal of the Korea Contents Association
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• v.12 no.8
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• pp.1-12
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• 2012

We develop the Spatio-Temporal Graph to imbue the historical context to the situations in a virtual world, and an ontology to enable a structural description of their elements such as the objects, relationships, and activities. In the time dimension the graph models all the temporal phases of the future besides the past and present in a comprehensive manner, and all the spatial aspects in an intuitive but efficient fashion. The overall architecture composing the Physical Layer, Logical Layer and Conceptual Layer which are integrated according to their interrelations allows events occurring in their corresponding worlds to be simulated in historical context. The S-T Graph could be used both to simulate the situations in the virtual world and to realize the knowledge systems of the virtual inhabitants to be used in judging and evaluating those situations. By adding temporal changes to the multi-layered architecture of our virtual world, this model lays a foundation for maximizing the diversity of situations in the simulation of a virtual world.

• The Journal of the Korea Contents Association
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• v.13 no.6
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• pp.9-19
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• 2013

In this paper, we develop a Spatio-Temporal graph as of a key component of our knowledge representation Scheme. We design an integrated representation scheme to depict not only present and past but future in parallel with the spaces in an effective and intuitive manner. An event in general occupies not only a space but a time. Hence a crucial premise for the simulation of virtual situations is to position events in the multi-dimensional context, that is, 3-D space extended by the temporal dimension. Furthermore an event tends to have physical, social and mental aspects intertwined. As a result we need diverse information structures and functions to model entities and relations associated with events and to describe situations in different stances or perspectives of the virtual agents. These structures and functions are implemented in terms of integrated and intuitive representation schemes at different levels such as Ontology View, Instance View, ST View, Reality View. The resulting multi-dimensional comprehensive knowledge structure accommodates multi-layered virtual world developing in the time to maximize the diversity of situations in the historical context. The viability of this knowledge representation scheme is demonstrated with a typical scenario applied to a simulator implemented based on the ST Graph. The virtual stage based on the ST graph can be used to provide natural contexts for situated learning or next-generation simulation games.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.5
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• pp.1909-1928
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• 2020

Predicting human mobility has always been an important task in Location-based Social Network. Previous efforts fail to capture spatial dependence effectively, mainly reflected in weakening the location topology information. In this paper, we propose a neural network-based method which can capture spatial-temporal dependence to predict the next location of a person. Specifically, we involve a graph convolutional network (GCN) based on a seq2seq framework to capture the location topology information and temporal dependence, respectively. The encoder of the seq2seq framework first generates the hidden state and cell state of the historical trajectories. The GCN is then used to generate graph embeddings of the location topology graph. Finally, we predict future trajectories by aggregated temporal dependence and graph embeddings in the decoder. For evaluation, we leverage two real-world datasets, Foursquare and Gowalla. The experimental results demonstrate that our model has a better performance than the compared models.

• Journal of the Korean Institute of Landscape Architecture
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• v.32 no.1
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• pp.47-56
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• 2004

Rapid economic development in Korea caused functions of city functions such as concentration of population, deterioration of the quality of living environment and traffic congestion. Korean cities have lost their identity becausr they are merged functionally and physically with neighboring cities, forming one mesa-city. Unified shape and disorganized streets of cities often cause confusion among foreigners and visitors. It is very difficult for them to find their image in strange cities. It is, however, important to correctly analyze the image and meaning of cities for understanding its identity. The purpose of this study is to develop a method to analyze the city image by focusing on some of the main cities in Korea. For this purpose, the adjective questionnaire and multi-dimension scaling (MDS) are applied to the analysis of city image. Image analysis graph by MDS can visually present the general and integrate images. The results of this study are summarized as follows: The important factors for interpretation of city image are historical and industrial character. Seoul, Taegu and Pusan have industrial and complex city images. Kongju has historical city image, while Changwon has a modern image. Chuncheon belongs to a soft and small image. Each city has an alternative solution against a negative image, according to the image analysis graph.

• Journal of Information Processing Systems
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• v.19 no.1
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• pp.130-138
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• 2023

The traffic flow in an urban area is affected by the date, weather, and regional traffic flow. The existing methods are weak to model the dynamic road network features, which results in inadequate long-term prediction performance. To solve the problems regarding insufficient capacity for dynamic modeling of road network structures and insufficient mining of dynamic spatio-temporal features. In this study, we propose a novel traffic flow prediction framework called shared spatio-temporal attention convolution optimization network (SSTACON). The shared spatio-temporal attention convolution layer shares a spatio-temporal attention structure, that is designed to extract dynamic spatio-temporal features from historical traffic conditions. Subsequently, the graph optimization module is used to model the dynamic road network structure. The experimental evaluation conducted on two datasets shows that the proposed method outperforms state-of-the-art methods at all time intervals.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.31-44
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• 2019

A graph theoretical model called Roman domination in graphs originates from the historical background that any undefended place (with no legions) of the Roman Empire must be protected by a stronger neighbor place (having two legions). It is applicable to military and commercial decision-making problems. A Roman dominating function for a graph G = (V, E) is a function $f:V{\rightarrow}\{0,1,2\}$ such that every vertex v with f(v)=0 has at least a neighbor w in G for which f(w)=2. The Roman domination number of a graph is the minimum weight ${\sum}_{v{\in}V}\;f(v)$ of a Roman dominating function. In order to deal a problem of a Roman domination-type defensive strategy under multiple simultaneous attacks, ${\acute{A}}lvarez$-Ruiz et al. [1] initiated the study of a new parameter related to Roman dominating function, which is called strong Roman domination. ${\acute{A}}lvarez$-Ruiz et al. posed the following problem: Characterize the graphs G with equal strong Roman domination number and Roman domination number. In this paper, we construct a family of trees. We prove that for a tree, its strong Roman dominance number and Roman dominance number are equal if and only if the tree belongs to this family of trees.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.33-42
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• 2006

In this paper, we study the theoretical and historical backgrounds with respect to isomorphism problem of combinatorial objects which is one of major problems in the theory of Combinatorics. And also, we introduce a partial result for isomorphism problem of Cayley objects over a finite field.

• Journal for History of Mathematics
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• v.27 no.4
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• pp.271-283
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• 2014

This study takes a look at Polya's analysis on Archimedes' "The Method" from a math-historical perspective. We, based on the elaboration of Polya's analysis, investigate the analytic geometric characteristics of Archimedes' "The Method" and discuss the way of using the characteristics in education of school calculus. So this study brings up the educational need of approach of teaching the definite integral by clearly disclosing the transition from length, area, volume etc into the length as an area function under a curve. And this study suggests the approach of teaching both merit and deficiency of the indivisibles method, and the educational necessity of making students realizing that the strength of analytic geometry lies in overcoming deficiency of the indivisibles method by dealing with the relation of variation and rate of change by means of algebraic expression and graph.