• Journal of the Society of Naval Architects of Korea
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• v.38 no.2
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• pp.79-86
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• 2001

This study shows an attempt to generate an assembly sequence and its model for a ship block assembly using the graph theory and graph algorithms. To generate the ship block assembly, we propose four levels of the ship block assembly model such as "geometry mode1", "relational model", "sequential mode1", and "hierarchical model". To obtain the relational model, we used surface and surface intersection algorithm. The sequential model that represents a possible assembly sequence is made by using several graph algorithms from the relational model. The hierarchical model will be constructed from the sequential model in order to represent the block assembly tree and so forth. The purpose of the hierarchical model is to define an assembly tree and to generate the Bill Of Material(BOM). Lastly, the validity of the method proposed in this study is examined with application to ship block assembly models of a single type and double type according to four models mentioned above.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.1
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• pp.358-377
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• 2015

In this paper, we propose a novel approach for trajectory recovery. Our system uses a triangulation procedure for skeletonization and graph theory to extract the trajectory. Skeletonization extracts the polyline skeleton according to the polygonal contours of the handwritten characters, and as a result, the junction becomes clear and the characters that are touching each other are separated. The approach for the trajectory recovery is based on graph theory to find the optimal path in the graph that has the best representation of the trajectory. An undirected graph model consisting of one or more strokes is constructed from a polyline skeleton. By using the polyline skeleton, our approach accelerates the process to search for an optimal path. In order to evaluate the performance, we built our own dataset, which includes testing and ground-truth. The dataset consist of thousands of handwritten characters and word images, which are extracted from five handwritten documents. To show the relative advantage of our skeletonization method, we first compare the results against those from Zhang-Suen, a state-of-the-art skeletonization method. For the trajectory recovery, we conduct a comparison using the Root Means Square Error (RMSE) and Dynamic Time Warping (DTW) in order to measure the error between the ground truth and the real output. The comparison reveals that our approach has better performance for both the skeletonization stage and the trajectory recovery stage. Moreover, the processing time comparison proves that our system is faster than the existing systems.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.545-557
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• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.513-522
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• 1994

A multi-dimensional design is most easily constructed via the amalgamation of one-dimensional component block designs. However, not all sets of component designs are compatible to be amalgamated. The conditions for compatibility are related to the concept of a complete matching in a graph. In this paper, we give sufficient conditions for unequal-replicate designs. Two types of conditions are proposed; one is based on the number of verices adjacent to at least one vertex and the other is ona a degree of vertex, in a bipartite graph. The former is an extension of the sufficient conditions of equal-replicate designs given by Dean an Lewis (1988).

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.295-309
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• 2020

Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.7
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• pp.448-453
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• 2006

We extend a parallel depth-first search (DFS) algorithm for planar graphs to deal with (non-planar) solid grid graphs, a subclass of non-planar grid graphs. The proposed algorithm takes time O(log n) with $O(n/sqrt{log\;n})$ processors in Priority PRAM model. In our knowledge, this is the first deterministic NC algorithm for a non-planar graph class.

• Industrial Engineering and Management Systems
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• v.10 no.4
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• pp.238-246
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• 2011

Given a directed graph, we can determine how the user's preference moves from one product item to another. In this graph called "preference transition network", each node represents the product item while its edge pointing to the other nodes represents the transition of user's preference. However, with the large number of items make the network become more complex, unclear and difficult to be interpreted. In order to address this problem, this paper proposes a visualization technique in preference transition analysis based on recency and frequency. By adapting these two elements, the semantic meaning of each item and its transition can be clearly identified by its different types of node size, color and edge style. The experiment in a sales data has shown the results of the proposed approach.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.689-701
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• 2021

The purpose of this paper is to optimize the number of source places required for the unique representation of the destination using the tools of graph theory. A subset S of vertices of a graph G is called a rational resolving set of G if for each pair u, v ∈ V - S, there is a vertex s ∈ S such that d(u/s) ≠ d(v/s), where d(x/s) denotes the mean of the distances from the vertex s to all those y ∈ N[x]. A rational resolving set is called minimal rational resolving set if no proper subset of it is a rational resolving set. In this paper we study varieties of minimal rational resolving sets defined on the basis of its complements and compute the minimum and maximum cardinality of such sets, respectively called as lower and upper rational metric dimensions for power of a path P_n analysing various possibilities.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.803-819
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• 2024

In our study, the integration of fuzzy graphs into classical graph theory gives rise to a novel concept known as "Fuzzy Super Subdivision." Let SS_f (G) be the fuzzy super subdivision graphs, by substituting a complete bipartite graph k_(2,m) (m = 1, 2, . . .) for each edge of a fuzzy graph. The attributes and properties of this newly proposed concept are briefly outlined, in addition to illustrative examples. Furthermore, significant findings are discussed on connectivity, size, degree and order of fuzzy super subdivision structures. To illustrate the practical implications of our approach, we present an application focused on analyzing the growth of infections in blood or urine samples using the Fuzzy Super Subdivision model.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.4A
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• pp.350-359
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• 2010

In this paper, we provide a subchannel allocation algorithm for a femtocell system with OFDMA. This algorithm aims to maximize the minimum number of allocated subchannels among all femtocells and in addition, to maximize the total usage of subchannels in all femtocells. The subchannel allocation algorithm consists of three steps: constructing an interference graph, coloring algorithm, and mapping subchannels to colors. In the first step, the femtocell system is modelled by an interference graph, in which each femtocell is modeled as a node and two nodes that interfere with each other are connected by an edge. Based on this interference graph, by using a coloring scheme and mapping subchannels to each color, we can allocate subchannels to each femtocell. Finally, the performance of this algorithm is provided by simulation.