• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1275-1281
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• 2011

Many authors studied cooperative games that arise from variants of dominating set games on graphs. In wireless networks, the connected dominating set is used to reduce routing table size and communication cost. In this paper, we introduce a connected dominating set game to model the cost allocation problem arising from a connected dominating set on a given graph and study its core. In addition, we give a polynomial time algorithm for determining the balancedness of the game on a tree, for finding a element of the core.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.297-309
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• 2006

In this paper, we consider cooperative games arising from integer domination problem on graphs. We introduce two games, ${\kappa}-domination$ game and its monotonic relaxed game, and focus on their cores. We first give characterizations of the cores and the relationship between them. Furthermore, a common necessary and sufficient condition for the balancedness of both games is obtained by making use of the technique of linear programming and its duality.

• East Asian mathematical journal
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• v.31 no.5
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• pp.717-725
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• 2015

Velzen introduced the rigid and relaxed dominating set games and showed that the rigid game being balanced is equivalent to the relaxed game being balanced in 2004. After then various variants of dominating set games were introduced and it was shown that for each variant, a rigid game being balanced is equivalent to a relaxed game being balanced. It is natural to ask if for any other variant of dominating set game, the balancedness of a rigid game and the balancedness of a relaxed game are equivalent. In this paper, we show that the answer for the question is negative by considering the rigid and relaxed paired-domination games, which is considered as a variant of dominating set games. We characterize the cores of both games and show that the rigid game being balanced is not equivalent to the relaxed game being balanced. In addition, we study the cores of paired-dominations games on paths and cycles.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1115-1121
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• 2007

In this paper, we consider cooperative games arising from integer total domination problem on graphs. We introduce two games, rigid integer total domination game and its relaxed game, and focus on their cores. We give characterizations of the cores and the relationship between them.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.265-275
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• 2006

In this paper, we introduce a fractional domination game arising from fractional domination problems on graphs and focus on its balancedness and concavity. We first characterize the core of the fractional domination game and show that its core is always non-empty taking use of dual theory of linear programming. Furthermore we study concavity of this game.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.871-881
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• 2008

In this paper, we study the core stability of the dominating set game which has arisen from the cost allocation problem related to domination problem on graphs. Let G be a graph whose neighborhood matrix is balanced. Applying duality theory of linear programming and graph theory, we prove that the dominating set game corresponding to G has the stable core if and only if every vertex belongs to a maximum 2-packing in G. We also show that for dominating set games corresponding to G, the core is stable if it is large, the game is extendable, or the game is exact. In fact, the core being large, the game being extendable and the game being exact are shown to be equivalent.

• The Journal of the Korea Contents Association
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• v.20 no.9
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• pp.271-284
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• 2020

Good reviews that Half-Life: Alyx received created a turning point for the vitalization of the VR market with an uncertain future due to the absence of a revenue model together with the increased sales of VR equipment. Based on previous studies, this study categorized the characteristics of VR games according to graphs, first-person system, interface, controller, interaction technology, sound and stories. The analysis results show that the seven elements corresponded with "interactions" and "virtual images," which represent the completion level of games as part of VR components, and were connected to one another, which led to the proposal of an upper-rank concept "presence" to put them together. "Immersiveness," which represents users' emotions as part of VR components, was analyzed with the immersion theory to assign tasks of proper difficulty level for users' abilities. In the research process, the Delphi technique and FGI were administered to a panel of 15 experts to ensure objectivity. Finally, "presence" and "immersiveness" are characteristics in proportion to each other and can be valid concepts in future analysis of VR games as well as Half-Life: Alyx, which led to the proposal a new concept framework called 'presence effects' by combining the two words.

• Journal of the Korea Society for Simulation
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• v.14 no.3
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• pp.21-31
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• 2005

In state-of-the-art games, characters can move in a goal-directed manner so that they can move to the goal position without colliding obstacles. Many path-finding methods have been proposed and implemented for these characters and most of them use the A* search algorithm. When .the map is represented with a regular grid of squares or a navigation mesh, it often takes a long time for the A* to search the state space because the number of cells used In the grid or the mesh increases for higher resolution. Moreover the A* search on the grid often causes a zigzag effect, which is not optimal and realistic. In this paper we propose to use visibility graphs to improve the search time by reducing the search space and to find the optimal path. We also propose a method of taking into account the size of moving characters in the phase of planning to prevent them from colliding with obstacles as they move. Simulation results show that the proposed method performs better than the grid-based A* algorithm in terms of the search time and space and that the resulting paths are more realistic.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.49-55
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• 2009

A cooperative game often arises from domination problem on graphs and the core in a cooperative game could be the optimal solution of a linear programming of a given game. In this paper, we define a {k}-fractional domination game which is a specific type of fractional domination games and find the core of a {k}-fractional domination game. Moreover, we may investigate the balancedness of a {k}-fractional domination game using a concept of a linear programming and duality. We also conjecture the concavity for {k}-fractional dominations game which is important problem to find the elements of the core.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1667-1690
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• 2018

We consider the minimum order of a graph G with a given lazy cop number $c_L(G)$. Sullivan, Townsend and Werzanski [7] showed that the minimum order of a connected graph with lazy cop number 3 is 9 and $k_3{\square}k_3$ is the unique graph on nine vertices which requires three lazy cops. They conjectured that for a graph G on n vertices with ${\Delta}(G){\geq}n-k^2$, $c_L(G){\leq}k$. We proved that the conjecture is true for k = 4. Furthermore, we showed that the Petersen graph is the unique connected graph G on 10 vertices with ${\Delta}(G){\leq}3$ having lazy cop number 3 and the minimum order of a connected graph with lazy cop number 4 is 16.