• Journal of the Korean Data and Information Science Society
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• 제22권6호
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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.

• 대한수학회지
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• 제43권2호
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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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• 제31권5호
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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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• 제18권4호
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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.

• 대한수학회보
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• 제43권2호
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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.

• 대한수학회지
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• 제45권3호
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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.

• 한국콘텐츠학회논문지
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• 제20권9호
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• pp.271-284
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• 2020

하프라이프 알릭스에 대한 시장의 호평과 VR장비 판매 증가는 수익모델의 부재로 미래가 불확실한 VR시장 활성화의 전환점이 될 수 있다. 이에 선행연구를 바탕으로 VR게임의 특성을 그래픽, 1인칭시스템, 인터페이스, 컨트롤러, 인터랙션 기술, 사운드, 스토리로 분류하고 분석하였다. 분석결과 7개 요소는 VR의 구성 요소 중 게임의 완성도를 의미하는 '상호작용'과 '가상이미지'에 해당하였으며 상호 연결되어 있어 이를 묶은 상위 개념인 '현존감'을 제안하였다. VR 구성요소로서 사용자의 감정을 나타내는 '몰입감'은 유저의 능력에 적절한 과제의 난이도를 부여하는 몰입이론으로 분석하였으며 연구 과정은 전문가 패널 15명에게 델파이 기법과 FGI를 실시하여 객관성 확보를 위해 노력하였다. 마지막으로 '현존감'과 '몰입감'은 비례하는 특성으로서 알릭스는 물론 앞으로 VR게임 분석에서도 계속 유효한 개념이 될 수 있으므로 두 단어를 합한 '프레즌스 이펙트'라는 개념적인 틀을 제안하였다.

• 한국시뮬레이션학회논문지
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• 제14권3호
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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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• 제20권1호
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• pp.49-55
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• 2009

게임이론 중 특히 협력게임은 종종 그래프에서의 지배문제로에 기인하며, 협력게임에서의 코어는 바로 이에 대한 선형프로그램의 최적해가 될 수 있다. 이 논문에서는, 분수 지배게임의 특수한 형태인 분수 지배게임을 새롭게 정의하며, 분수 지배게임의 코어를 찾는다. 더욱이 선형 프로그래밍과 그 쌍대성 개념을 이용하여 {k}-분수 지배게임의 균형성을 조사한다. 또한 코어의 원소를 찾기 위한 중요한 문제가 되는 오목성에 있어서 분수 지배게임도 오목성을 가질 것이라고 추축해본다.

• 대한수학회보
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• 제55권6호
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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.