• Proceedings of the Korea Information Processing Society Conference
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• 2011.04a
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• pp.1240-1242
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• 2011

인터넷의 발달로 데이터의 양이 기하급수적으로 증가함에 따라 대용량 데이터를 효율적으로 검색하는 top k 질의 처리의 중요성이 커지고 있다. top k 는 릴레이션에서 가장 높은 (또는 가장 낮은) 스코어를 가지는 k 개의 튜플을 반환하는 방법으로, 스코어는 사용자가 정의한 스코어링 함수를 통해 계산된다. 효율적인 top k 질의 처리를 위해서는 전체 데이터 집합 중 최소한의 서브집합만 읽어서 k 개의 결과를 구할 수 있어야 한다. 이를 위해 기존 연구들은 다양한 방법의 인덱스 생성방법을 제안했다. 본 논문에서는 그 중에서 convex hull 을 사용하여 layer list 를 생성하는 기존 연구를 조사하고 문제점을 도출한다. 기존 연구 문제점 분석은 향후 연구인 스카이라인을 사용하는 top k 질의 처리 연구의 기반이 될 것으로 예상한다.

• Journal of applied mathematics & informatics
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• v.2 no.2
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• pp.83-95
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• 1995

Given a closed subset of the family $S^{*}(\alpha)$ of functions starlike of order $\alpha$, a continuous Frechet differentiable functional J, is constructed with this collection as the solution set to the extremal problem ReJ(f) over $S^{*}(\alpha)$. The support points of $S^{*}(\alpha)$ is completely characterized and shown to coincide with the extreme points of its convex hulls. Given any finite collection of support points of $S^{*}(\alpha)$ a continuous linear functional J, is constructed with this collection as the solution set to the extremal problem ReJ(f) over $S^{*}(\alpha)$.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.51
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• pp.21-28
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• 1999

The TSP(Traveling Salesman Problem) is one of the most widely studied problems in combinatorial optimization. The most common interpretation of TSP is finding a shortest Hamiltonian tour of all cities. The objective of this paper proposes a new heuristic algorithm MCH(Multi-Convex hulls Heuristic). MCH is a algorithm for finding good approximate solutions to practical TSP. The MCH algorithm is using the characteristics of the optimal tour. The performance results of MCH algorithm are superior to others algorithms (NNH, CCA) in CPU time.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.1-16
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• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".

• Journal of information and communication convergence engineering
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• v.8 no.1
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• pp.59-63
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• 2010

The shortest path between two points inside a simple polygon P is a minimum-length path among all paths connecting them which don't pass by the exterior of P. A linear time algorithm for computing the shortest path in a general simple polygon requires triangulating a given polygon as preprocessing. The linear time triangulating is known to very complex to understand and implement it. It is also inefficient in case that the input without very large size is given because its time complexity has a big constant factor. Two points of a polygon P are said to be L-visible from each other if they can be joined by a simple chain of at most two rectilinear line segments contained in P completely. An L-visible polygon P is a polygon such that there is a point from which every point of P is L-visible. We present the customized optimal shortest path algorithm for an L-visible polygon. Our algorithm doesn't require triangulating as preprocessing and consists of simple procedures such as construction of convex hulls and operations for convex polygons, so it is easy to implement and runs very fast in linear time.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.4
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• pp.753-758
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• 2017

The ray-shooting problem is to find the first intersection point on the surface of given geometric objects where a ray moving along a straight line hits. Since rays are usually given in the form of queries, this problem is typically solved as follows. First, a data structure for a collection of objects is constructed as preprocessing. Then, the answer for each query ray is quickly computed using the data structure. In this paper, we consider the ray-shooting problem about the set of vertical line segments on the x-axis. We present a new data structure called a convex layer tree for n vertical line segments given by input. This is a tree structure consisting of layers of convex hulls of vertical line segments. It can be constructed in O(n log n) time and O(n) space and is easy to implement. We also present an algorithm to solve each query in O(log n) time using this data structure.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.3
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• pp.513-518
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• 2016

This paper presents a fast 3D mesh generation method using projection for line laser-based 3D scanners. The well-known method for 3D mesh generation utilizes convex hulls for 4D vertices that is converted from the input 3D vertices. This 3D mesh generation for a large set of vertices requires a lot of time. To overcome this problem, the proposed method takes (${\theta}-y$) 2D depth map into account. The 2D depth map is a projection version of 3D data with a form of (${\theta}$, y, z) which are intermediately acquired by line laser-based 3D scanners. Thus, our 2D-based method is a very fast 3D mesh generation method. To evaluate our method, we conduct experiments with intermediate 3D vertex data from line-laser scanners. Experimental results show that the proposed method is superior to the existing method in terms of mesh generation speed.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.2
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• pp.369-374
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• 2010

The shortest path between two points inside a simple polygon P is a minimum-length path among all paths connecting them which don't pass by the exterior of P. A linear time algorithm for computing the shortest path in a general simple polygon requires triangulating a polygon as preprocessing. The linear time triangulating is known to very complex to understand and implement it. It is also inefficient in case that the input without very large size is given because its time complexity has a big constant factor. In this paper, we present the customized shortest path algorithm for a segment-visible polygon which is a simple polygon weakly visible from an internal line segment. Our algorithm doesn't require triangulating as preprocessing and consists of simple procedures such as construction of convex hulls, so it is easy to implement and runs very fast in linear time.