• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.85-101
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• 2018

Let S be a polynomial ring over a field K, with a monomial order ${\prec}$, and let I be an unmixed graded ideal of S. In this paper we study two functions associated to I: The minimum distance function ${\delta}_I$ and the footprint function $fp_I$. It is shown that ${\delta}_I$ is positive and that $fp_I$ is positive if the initial ideal of I is unmixed. Then we show that if I is radical and its associated primes are generated by linear forms, then ${\delta}_I$ is strictly decreasing until it reaches the asymptotic value 1. If I is the edge ideal of a Cohen-Macaulay bipartite graph, we show that ${\delta}_I(d)=1$ for d greater than or equal to the regularity of S/I. For a graded ideal of dimension ${\geq}1$, whose initial ideal is a complete intersection, we give an exact sharp lower bound for the corresponding minimum distance function.

• Journal of the Korea Society for Simulation
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• v.15 no.2
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• pp.31-39
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• 2006

The visibility graph is a well-known method for efficient path-finding with the minimum search space modelling the game world. The generalized visibility graph is constructed on the expanded obstacle boundaries to eliminate the "wall-hugging" problem which is a major disadvantage of using the visibility graph. The paths generated by the generalized visibility graph are guaranteed to be near optimal and natural-looking. In this paper we propose the method to apply the generalized visibility graph efficiently for game characters who moves among static obstacles between varying start and goal points. Even though the space is minimal once the generalized visibility graph is constructed, the construction itself is time-consuming in checking the intersection between every two links connecting nodes. The idea is that we build the map for static obstacles first and then incorporate start and goal nodes quickly. The incorporation of start and goal nodes is the part that must be executed repeatedly. Therefore we propose to use the rotational plane-sweep algorithm in the computational geometry for incorporating start and goal nodes efficiently. The simulation result shows that the execution time has been improved by 39%-68% according to running times in the game environment with multiple static obstacles.

• Journal of Computational Design and Engineering
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• v.3 no.1
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• pp.14-23
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• 2016

The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.2
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• pp.401-407
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• 2016

We can consider the following problems for two given points p and q in a simple polygon P. (1) Compute the set of points of P which are visible from both p and q. (2) Compute the set of points of P which are visible from either p or q. They are corresponding to the problems which are to compute the intersection and the union of two visibility polygons. In this paper, we consider algorithms for solving these problems on a reconfigurable mesh(in short, RMESH). The algorithm in [1] can compute the intersection of two general polygons in constant time on an RMESH with size O($n^3$), where n is the total number of vertices of two polygons. In this paper, we construct the planar subdivision graph in constant time on an RMESH with size O($n^2$) using the properties of the visibility polygon for preprocessing. Then we present O($log^2n$) time algorithms for computing the union as well as the intersection of two visibility polygons, which improve the processor-time product from O($n^3$) to O($n^2log^2n$).

• Water for future
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• v.12 no.2
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• pp.56-62
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• 1979

Many methods of estimating design floods from rainfall data involve a trial and error procedure to determine the duration of the design rainfall, which is very complicated and time-consuming. In this study, an effort was given to derive an analytical expression for estimating the appropriate duration for use with a particular unit hydrograph. According to the so-derived analytical expression the coordinateds of hvdrograph curve and rainfall curve for the Musim Representative Basin were computed and then plotted on a same scal graph paper on which the critical durations of design rainfall excess of various recurrence intervals were determined by the point of intersection of the tow curves.

• Proceedings of the KIEE Conference
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• 1988.07a
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• pp.591-594
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• 1988

A three-step heuristic algorithm for PLA column folding and row folding of column-folded PLA is presented, which is significantly faster than the earlier works and provides nearly optimal results. The three steps are i) min-cut partition of vertices in the column (or row) intersection graph, ii) determination of products' order using Fiduccia's min-net cut algorithm, and iii) head-tail pairing for column folding, while some heuristics are proposed for deciding row folding pairs. The time complexity of this algorithm is O($n^{2}$log n) compared to the O($n^{3}$) - O($n^{4}$) of the earlier works.$^[2][3][9]$ For a test PLA with 23 inputs, 19 outputs and 52 products, the number of column folding pairs obtained using this algorithm is 20 which is optimal, as compared to 17 in a previous work.

• Proceedings of the Korea Information Processing Society Conference
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• 2001.04a
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• pp.349-352
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• 2001

웹 기반 협동설계시스템은 인터넷망과 웹브라우저를 이용하여 공유된 가상 공간에서 협동작업이 이루어지도록 한다. 이때 공유 오브젝트는 3D 도형이 되며, 사용자가 임의의 오브젝트를 선택하여 조작하기 위하여 picking이 효과적으로 이루어져야 한다. 본 논문에서는 오브젝트의 picking이 마우스 포인터에서의 ray와 오브젝트간에 intersection을 계산하는 방법 외에 Java 3D API를 이용하여 scene graph의 노드에 picking 속성을 주는 방법, bounds를 설정하는 방법, picking test의 범위를 한정하는 방법을 사용하여 computation의 부담을 줄이고 효과적인 picking이 이루어지도록 한다.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.883-898
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• 2013

The purpose of this study is to examine that high school students recognize mathematical situation when they are requested for changing identical mathematics situations into different situations. The results of the study are followings. First, percentage of correct answers to the questions of turning equal mathematical situation into function is higher than the one of turning equal mathematical situation into equation and inequality. As a result of individual interview for comprehensibility of the students on these relations, it is found that if degree goes up and there is different expressions of questionaries although mathematical situation is identical, it affects comprehensibility of the subjects. Second, we found that they cannot understand identical mathematics situations because they have trouble in drawing graph or applying to get the answer while many students understand a point of intersection on the graph as a correct answer. Third, As a result of individual interview for comprehensibility of the students on relation between equation, inequality and function, we found that students manage to get correct answer even without perfect comprehensibility on this relation.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.4
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• pp.89-97
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• 2024

The problem of the spokes puzzle(SP), which connects the spokes(edges) required by the wheel axis (hub, vertex) without intersection to form a network in which all the hubs are connected, can be said to be a wasteland of research. For this problem, there is no algorithm that presents a brute-force search or branch-and-bound method that takes exponential time. This paper proposes an algorithm to plot a lattice graph with cross-diagonal lines of m×n for a given SP and to pruning(delete) the surplus edges(spokes). The proposed algorithm is a simple way to select an edge of a hub whose number of edges matches the hub requirement and delete the edge crossing it. If there is no hub with an edge that meets the hub requirement, a strategy was adopted to preferentially delete(pruning) the edge of the hub with the maximum amount of spare. As a result of applying the proposed algorithm to 20 benchmarking experimental data, it was shown that a solution that minimizes the number of trials and errors can be obtained for all problems.

• Journal of Korean Society of Transportation
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• v.5 no.2
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• pp.81-95
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• 1987

In line with the continued growth of car ownership, the traffic problems in central area of metropoles such as Seoul would become increasingly degraded. comparing with most western cities, the problems in Seoul are characterized by the improportionately high rates of intersection delay, station congestion, traffic accidents caused by weaving conflicts and pedestrian congestion. It is caused by the lack of flexibility I street network, which is prerequisite for upholding the efficacy of traffic management and control, resulted from the simplicity of network graph in terms of connectivity, street density and distribution by width. This pattern has been resulted from the prolonged policy pursuing the street-widening of the nagging bottleneck in such a short period since the 1950s, comparing that most western cities had undergone over several centuries an age of horse-and-vehicle transportation. In order to improve the expected traffic problems in central area over the coming periods of motorization, it is imperative to restructure the street network in Central Seoul so that the efficacy of traffic management and control may be operative. Based upon the long-range planning the street network should be restructured by stages so that cenral traffic may be controled by one-way operation and most through-traffic be detoured around fringe area.