• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.6
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• pp.674-677
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• 2004

This paper deals with a systematic approach for the construction of the fixed-delay tree search (FDTS) detector in the intersymbol interference channel. The approach is based on the efficient multi-dimensional space partitioning. The Voronoi diagram (VoD) and the Delaunay tessellation (DT) of the multi-dimensional space are applied to implement the algorithm. In the proposed approach, utilizing the geometric information contained in the VOD/DT, the relative location of the observation sequence is determined which has been shown to reduce the implementation complexity. Detailed construction procedures are discussed followed by an example from the intersymbol interference communication channel.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.129-138
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• 1997

In this paper, the problem for choosing design points in the two dimensional case is condidered. In the one dimensional case, given the design density function, we can choose design points using the quantile function. However, in the two dimensional case, there is no clear definition of the percentile. Therefore, the idea of choosing design points in the univariate case can not be applied directly to the two dimensional case. We convert this problem into an optimization problem using the Voronoi diagram.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.6
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• pp.687-693
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• 2012

In this paper, we propose a optimal deployment method for cooperative exploration of swarm robots. The proposed method consists of two parts such as optimal deployment and path planning. The optimal area deployment is proposed by the K-mean Algorithm and Voronoi tessellation. The path planning is proposed by the potential field method and A* Algorithm. Finally, the numerical experiments demonstrate the effectiveness and feasibility of the proposed method.

• Journal of Korea Multimedia Society
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• v.9 no.2
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• pp.139-150
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• 2006

A schematic map is a special purpose map which is generated to recognize it's objects easily and conveniently via simplifying and highlighting logical geometric information of a map. To manufacture the schematic map with road, label and icon, we must generate simplified route map and replace many geometric objects. Performing a give task, however, there are an amount of overlap areas between geometric objects whenever we process the replacement of geometry objects. Therefore we need replacing geometric objects without overlap. But this work requires much computational resources, because of the high complexity of the original geometry map. We propose the schematic map generation system whose map consists of icons and label. The proposed system has following steps: 1) eliminating kinks that are least relevant to the shape of polygonal curve using DCE(Discrete Curve Evolution) method. 2) making an evenly distributed route using CVT(Centroidal Voronoi Tessellation) and Grid snapping method. Therefore we can keep the structural information of the route map from CVT method. 3) replacing an icon and label information with collision avoidance algorithm. As a result, we can replace the vertices with a uniform distance and guarantee the available spaces for the replacement of icons and labels. We can also minimize the overlap between icons and labels and obtain more schematized map.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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• pp.141-159
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• 2009

In this article, we consider a weighted CVT-based reduced-order modelling for Burgers equation. Brief review of the CVT (centroidal Voronoi tessellation) approaches to reduced-order bases are provided. In CVT-reduced order modelling, we start with a snapshot set just as is done in a POD (Proper Orthogonal Decomposition)-based setting. So far, the CVT was researched with uniform density ($\rho$(y) = 1) to determine the basis elements for the approximatin subspaces. Here, we shall investigate the technique of CVT with nonuniform density as a procedure to determine the basis elements for the approximating subspaces. Some numerical experiments including comparison of two CVT (CVT-uniform and CVT-nonuniform)-based algorithm with numerical results obtained from FEM(finite element method) and POD-based algorithm are reported.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.1-1
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• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.419-425
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• 2012

This paper presents an approach to implement the behaviors of multi-robots responding to user's input characters. The robots are appropriately displaced to express any input characters. Using our method, any user can easily and friendly control multirobots. The responses of the robots to the user's input are intuitive. We utilize the centroidal Voronoi algorithm and the continuoustime Lloyd algorithm, which have popularly been used for the optimal sensing coverage problems. Collision protection is considered to be applied for real robots. LED sensors are used to identify positions of multi-robots. Our approach is evaluated through experiments with five mobile robots. When a user draw alphabets, the robots are deployed correspondingly. By checking position errors, the feasibility of our method is validated.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.43 no.1 s.343
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• pp.57-70
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• 2006

This paper descWireless Sensor Network consisting of a number of small sensors with transceiver and data processor is an effective means for gathering data in a variety of environments. The data collected by each sensor is transmitted to a processing center that use all reported data to estimate characteristics of the environment or detect an event. This process must be designed to conserve the limited energy resources of the sensor since neighboring sensors generally have the data of similar information. Therefore, clustering scheme which sends aggregated information to the processing center may save energy. Existing multi-hop cluster energy consumption modeling scheme can not estimate exact energy consumption of an individual sensor. In this paper, we propose a new cluster energy consumption model which modified existing problem. We can estimate more accurate total energy consumption according to the number of clusterheads by using Voronoi tessellation. Thus, we can realize an energy efficient cluster formation. Our modeling has an accuracy over $90\%$ when compared with simulation and has considerably superior than existing modeling scheme about $60\%.$ We also confirmed that energy consumption of the proposed modeling scheme is more accurate when the sensor density is increased.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.50.1-50.1
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• 2015

We present a new hydrodynamic simulation based on the unstructured moving mesh scheme. The simulation utilizes the Voronoi tessellation technique that produces polygonal cells composed of, on average, 13 surfaces each in 3D. We devise the incremental expanding method (IEM) and hybrid-neighbor searching algorithm and achieve the CPU time just proportional to the number of particles, i.e., O(N). We show the results of requisite tests for hydrodynamic simulations and demonstrate superiority of our code over the conventional codes using the stationary meshes. The applications in the context of cosmological and galactic simulations are also discussed.

• East Asian mathematical journal
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• v.34 no.5
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• pp.661-681
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• 2018

In this paper, we discuss a reduced-order modeling for the Benjamin-Bona-Mahony-Burgers (BBMB) equation and its application to a distributed feedback control problem through the centroidal Voronoi tessellation (CVT). Spatial distcritization to the BBMB equation is based on the finite element method (FEM) using B-spline functions. To determine the basis elements for the approximating subspaces, we elucidate the CVT approaches to reduced-order bases with snapshots. For the purpose of comparison, a brief review of the proper orthogonal decomposition (POD) is provided and some numerical experiments implemented including full-order approximation, CVT based model, and POD based model. In the end, we apply CVT reduced-order modeling technique to a feedback control problem for the BBMB equation.