• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.4
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• pp.233-241
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• 2014

This paper suggests a fast minimum spanning tree algorithm which simplify the original graph to 2-edge connected graph, and using the cycling property. Borůvka algorithm firstly gets the partial spanning tree using cycle property for one-edge connected graph that selects the only one minimum weighted edge (e) per vertex (v). Additionally, that selects minimum weighted edge between partial spanning trees using cut property. Kruskal algorithm uses cut property for ascending ordered of all edges. Reverse-delete algorithm uses cycle property for descending ordered of all edges. Borůvka and Kruskal algorithms always perform |e| times for all edges. The proposed algorithm obtains 2-edge connected graph that selects 2 minimum weighted edges for each vertex firstly. Secondly, we use cycle property for 2-edges connected graph, and stop the algorithm until |e|=|v|-1 For actual 10 benchmark data, The proposed algorithm can be get the minimum spanning trees. Also, this algorithm reduces 60% of the trial number than Borůvka, Kruskal and Reverse-delete algorithms.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.3
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• pp.51-61
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• 2012

This paper suggests an algorithm that obtains Directed Graph Minimum Spanning Tree (DMST), using Prim MST algorithm which is Minimum Spanning Tree (MST) of undirected graph. At first, I suggested the Prim DMST algorithm that chooses Minimum Weight Arc(MWA) from out-going nodes from each node, considering differences between undirected graph and directed graph. Next, I proved a disadvantage of Prim DMST algorithm and Chu-Liu/Edmonds DMST (typical representative DMST) of not being able to find DMST, applying them to 3 real graphs. Last, as an algorithm that can always find DMST, an advanced Prim DMST is suggested. The Prim DMST algorithm uses a method of choosing MWA among out-going arcs of each node. On the other hand, the advanced Prim DMST algorithm uses a method of choosing a coinciding arc from the out-going and in-going arcs of each node. And if there is no coinciding arc, it chooses MWA from the out-going arcs from each node. Applying the suggested algorithm to 17 different graphs, it succeeded in finding the same DMST as that found by Chu-Liu/Edmonds DMST algorithm. Also, it does not require such a complicated calculation as that of Chu-Liu/Edmonds DMST algorithm to delete the cycle, and it takes less time for process than Prim DMST algorithm.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.4
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• pp.107-116
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• 2013

This algorithm suggests a method in which a minimum spanning tree can be obtained fast by reducing the number of an algorithm execution. The suggested algorithm performs a select-and-delete process. In the select process, firstly, it performs Borůvka's first stage for all the vertices of a graph. Then it re-performs Borůvka's first stage for specific vertices and reduces the population of the edges. In the delete process, it deletes the maximum weight edge if any cycle occurs between the 3 edges of the edges with the reduced population. After, among the remaining edges, applying the valency concept, it gets rid of maximum weight edges. Finally, it eliminates the maximum weight edges if a cycle happens among the vertices with a big valency. The select-and-delete algorithm was applied to 9 various graphs and was evaluated its applicability. The suggested select process is believed to be the vest way to choose the edges, since it showed that it chose less number of big edges from 6 graphs, and only from 3 graphs, comparing to the number of edges that is to be performed when using MST algorithm. When applied the delete process to Kruskal algorithm, the number of performances by Kruskal was less in 6 graphs, but 1 more in each 3 graph. Also, when using the suggested delete process, 1 graph performed only the 1st stage, 5 graphs till 2nd stage, and the remaining till 3rd stage. Finally, the select-and-delete algorithm showed its least number of performances among the MST algorithms.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.12
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• pp.1682-1687
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• 2020

We study the problem of sampling a subset of nodes of graphs for bandlimited graph signals such that the signal values on the sampled nodes provide the most information in order to reconstruct the original graph signal. Instead of directly minimizing the reconstruction error, we focus on minimizing the upper bound of the reconstruction error to reduce the complexity of the selection process. We further simplify the upper bound by applying useful approximations to propose a low-weight greedy selection process that is iteratively conducted to find a suboptimal sampling set. Through the extensive experiments for various graphs, we inspect the performance of the proposed algorithm by comparing with different sampling set selection methods and show that the proposed technique runs fast while preserving a competitive reconstruction performance, yielding a practical solution to real-time applications.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.1
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• pp.1-19
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• 2021

The graph-based tag recommendation algorithm FolkRank can effectively utilize the relationships between three entities, namely users, items and tags, and achieve better tag recommendation performance. However, FolkRank does not consider the internal relationships of user-user, item-item and tag-tag. This leads to the failure of FolkRank to effectively map the tagging behavior which contains user neighbors and item neighbors to a tripartite graph. For item-item relationships, we can dig out items that are very similar to the target item, even though the target item may not have a strong connection to these similar items in the user-item-tag graph of FolkRank. Hence this paper proposes an improved FolkRank algorithm named FolkRank++, which fully considers the user-user and item-item internal relationships in tag recommendation by adding the correlation information between users or items. Based on the traditional FolkRank algorithm, an initial weight is also given to target user and target item's neighbors to supply the user-user and item-item relationships. The above work is mainly completed from two aspects: (1) Finding items similar to target item according to the attribute information, and obtaining similar users of the target user according to the history behavior of the user tagging items. (2) Calculating the weighted degree of items and users to evaluate their importance, then assigning initial weights to similar items and users. Experimental results show that this method has better recommendation performance.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1309-1318
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• 2009

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) $\rightarrow$ {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices $\upsilon_1,\;\upsilon_2,\;{\ldots},\;\upsilon_k$ with $f(\upsilon_i)$ = 2 for i = 1, 2, $\ldot$, k. The weight of a Roman k-dominating function is the value f(V (G)) = $\sum_{u{\in}v(G)}$ f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number ${\gamma}_{kR}$(G) of G. Note that the Roman 1-domination number $\gamma_{1R}$(G) is the usual Roman domination number $\gamma_R$(G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.8
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• pp.3203-3215
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• 2015

Due to the high growth of SNS population, service scalability is one of the critical issues to be addressed. The cloud environment provides the flexible computing and storage resources for services deployment, which fits the characteristics of scalable SNS deployment. However, if the SNS related information is not properly placed, it will cause unbalance load and heavy transmission cost on the storage virtual machine (VM) and cloud data center (CDC) network. In this paper, we characterize the SNS into a graph model based on the users' associations and interest correlations. The node weight represents the degree of associations, which can be indexed by the number of friends or data sources, and the link weight denotes the correlation between users/data sources. Then, based on the SNS graph, the two-step algorithm is proposed in this paper to determine the placement of SNS related data among VMs. Two k-means based clustering schemes are proposed to allocate social data in proper VM and physical servers for pre-configured VM and dynamic VM environment, respectively. The experimental example was conducted and to illustrate and compare the performance of the proposed schemes.

• Korean Journal of Applied Biomechanics
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• v.12 no.1
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• pp.205-219
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• 2002

This research seeks to identify the plantar pressure distribution graph and change in force in connection with effective golf drive strokes and thus to help ordinary golfers have appropriate understanding on the moving of the center of weight and learn desirable drive swing movements. To this end, we conducted surveys on five excellent golfers to analyze the plantar pressure applied when performing golf drive strokes, and suggested dynamic variables quantitatively. 1) Our research presents the desire movements as follows. For the time change in connection with the whole movement, as a golfer raises the club head horizontally low above ground from the address to the top swing, he makes a semicircle using the left elbow joint and shaft and slowly turns his body, thus lengthening the time. And, as the golfer twists the right waist from the middle swing to the impact with the head taking address movement, and does a quick movement, thus shortening the time. 2) For the change in pressure distribution by phase, to strike a strong shot with his weight imposed from the middle swing to the impact, a golfer uses centrifugal force, fixes his left foot, and makes impact. This showed greater pressure distribution on the left sole than on the right sole. 3) For the force distribution graph by phase, the force in the sole from the address to halfway swing movements is distributed to the left foot with 46% and to the right foot with 54%. And, with the starting of down swing, as the weight shifts to the left foot, the force is distributed to the left sole with 58%. Thus, during the impact and follow through movements, it is desirable for a golfer to allow his left foot to take the weight with the right foot balancing the body. 4) The maximum pressure distribution and average of the maximum force in connection with the whole movement changed as the left (foot) and right (foot) supported opposing force, and the maximum pressure distribution also showed much greater on the left sole.

• Journal of the Korea Computer Graphics Society
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• v.29 no.4
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• pp.17-24
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• 2023

In computer graphics and computer vision research and its applications, various representations of 3D objects, such as point clouds, voxels, or triangular meshes, are used depending on the purpose. The need for animating characters using these representations is also growing. In a typical animation pipeline called skeletal animation, "skinning weight painting" is required to determine how joints influence a vertex on the character's skin. In this paper, we introduce a neural network for automatically performing skinning weight painting for characters represented in various formats. We utilize signed distance fields (SDF) to handle different representations and employ graph neural networks and multi-layer perceptrons to predict the skinning weights for a given point.

• 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.