• Proceedings of the KSME Conference
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• 2003.04a
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• pp.822-827
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• 2003

Topological maps have drawn more attention recently because they are compact, provide natural interfaces, and are applicable to path planning easily. To build a topological map incrementally, Voronoi diagram was used by many researchers. The Voronoi diagram, however, has difficulty in applying to arbitrarily shaped objects and needs long computation time. In this paper, we present a new method for global topological map from the local topological maps incrementally. The local topological maps are created through a thinning algorithm from a local grid map, which is built based on the sensor information at the current robot position. A thinning method requires simpler computation than the Voronoi diagram. Localization based on the topological map is usually difficult, but additional nodes created by the thinning method can improve localization performance. A series of experiments have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can create satisfactory topological maps.

• The KIPS Transactions:PartA
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• v.19A no.4
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• pp.169-174
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• 2012

We present an algorithm that computes a 3 dimensional Voronoi diagram for a protein molecule in this paper. The molecule is represented as a set of spheres with van der Waals radii. The Voronoi diagram is constructed in the 3D space by finding the voxels containing it. For the feasibility of the computation, we represent the molecule as a BVH (bounding volume hierarchy), and our system is accelerated by modern graphics hardware with CUDA programming support. Compared to single-core CPU implementations, experimental results show 323 times faster performance in the computation time, when the space is partitioned into $2^{24}$ voxels.

• Journal of Korea Multimedia Society
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• v.3 no.3
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• pp.298-308
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• 2000

We present an efficient algorithm for finding the sequence of extreme vortices of a moving regular convex polyhedron of with respect to a fixed plane H.. The algorithm utilizes the spherical Voronoi diagram that results from the outward unit normal vectors nF$_{i}$ 's of faces of P. It is well-known that the Voronoi diagram of n sites in the plane can be computed in 0(nlogn) time, and this bound is optimal. However. exploiting the convexity of P, we are able to construct the spherical Voronoi diagram of nF$_{i}$ ,'s in O(n) time. Using the spherical Voronoi diagram, we show that an extreme vertex problem can be transformed to a spherical point location problem. The extreme vertex problem can be solved in O(logn) time after O(n) time and space preprocessing. Moreover, the sequence of extreme vertices of a moving regular convex polyhedron with respect to H can be found in (equation omitted) time, where m$^{j}$ $_{k}$ (1$\leq$j$\leq$s) is the number of edges of a spherical Voronoi region sreg(equation omitted) such that (equation omitted) gives one or more extreme vertices.

• Spatial Information Research
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• v.15 no.3
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• pp.203-218
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• 2007

The purpose of this article is to set up the scientific and reasonable norm of location and service area determination instead of the pro-administrative lacking availability, so as to propose more practical and reasonable standard of space unit for the location of facilities. This article has accepted the method of Voronoi Diagram as a new scientific and reasonable criteria. The article chooses and realizes a model that can propose a new service area, transform and apply to improve its reality, and assesses which has more reality and compatibility by comparing the models. The result from this procedure can be adapted in objectification of the service area determination and formation of the standard space unit.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.257-277
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• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.11
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• pp.3896-3915
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• 2014

The Reverse k Nearest Neighbor (RkNN) query is valuable for finding objects influenced by a specific object and is widely used in both scientific and commercial systems. However, the influence level of each object is unknown, information that is critical for some applications (e.g. target marketing). In this paper, we propose a new query type, Ordered Reverse k Nearest Neighbor (ORkNN), and make efforts to adapt it in an on-demand scenario. An Order-k Voronoi diagram based approach is used to answer ORkNN queries. In particular, for different values of k, we pre-construct only one Voronoi diagram. Algorithms on both the server and the clients are presented. We also present experimental results that suggest our proposed algorithms may have practical applications.

• International Journal of Internet, Broadcasting and Communication
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• v.15 no.2
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• pp.22-30
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• 2023

The portable mobile devices with high performance and high speed 5G network activate and explode the demands for ubiquitous information services that remove the limitations of time for the communication and places to request for the information. NN (Nearest Neighbor) search is one of the most important types of queries to be processed efficiently in the information services. Various indexes have been proposed to support efficient NN search in the wireless broadcast system. The indexes adopting Hilbert curve, grid partition or Voronoi diagram enable the clients to search for NN quickly in the wireless broadcast channel. It is necessary that an efficient means to evaluate the performances of various indexes. In this paper, we propose an open framework that can adopt a variety of indexing schemes and evaluate and compare the performances of them. The proposed framework is organized with open and flexible structure that can adopt hybrid indexing schemes extensible to Voronoi diagram as well as simple indexing schemes. With the implemented framework, we demonstrate the efficiency and scalability and flexibility of the proposed framework by evaluating various indexing schemes for NN query.

• Journal of Information Processing Systems
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• v.7 no.1
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• pp.17-28
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• 2011

Despite the fact that the deployment of sensor networks and target tracking could both be managed by taking full advantage of Voronoi diagrams, very little few have been made in this regard. In this paper, we designed an optimized barrier coverage and an energy-efficient clustering algorithm for forming Vonoroi-based Wireless Sensor Networks(WSN) in which we proposed a mobile target tracking scheme (CTT&MAV) that takes full advantage of Voronoi-diagram boundary to improve detectability. Simulations verified that CTT&MAV outperforms random walk, random waypoint, random direction and Gauss-Markov in terms of both the average hop distance that the mobile target moved before being detected and lower sensor death rate. Moreover, we demonstrate that our results are robust as realistic sensing models and also validate our observations through extensive simulations.

• Proceedings of the Korean Society of Computer Information Conference
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• 2016.01a
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• pp.283-284
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• 2016

사물인터넷이란 인간의 일상생활에 사용 중인 가전제품, 의료기기, 기타 센서 부착 기기들이 인터넷에 연결되어 스스로 통신하고 제어하는 환경이다. 본 논문에서는 사물인터넷을 구성하는 각 사물들 간의 효율적인 통신을 위해 센터노드를 설정하고 각 사물들이 센터 노드를 중계기로 활용하여 다른 사물들과 효과적인 통신할 때 보로노이 다이어그램을 적용하는 방법을 제안한다.