• International Journal of CAD/CAM
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• v.8 no.1
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• pp.21-28
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• 2009

In the present work, an attempt has been made to construct branching surface from 2-D contours, which are given at different layers and may have branches. If a layer having more than one contour and corresponds to contour at adjacent layers, then it is termed as branching problem and approximated by adding additional points in between the layers. Firstly, the branching problem is converted to single contour case in which there is no branching at any layer and the final branching surface is obtained by skinning. Contours are constructed from the given input points at different layers by energy-based B-Spline approximation. 3-D curves are constructed after adding additional points into the contour points for all the layers having branching problem by using energy-based B-Spline formulation. Final 3-D surface is obtained by skinning 3-D curves and 2-D contours. There are three types of branching problems: (a) One-to-one, (b) One-to-many and (c) Many-to-many. Oneto-one problem has been done by plethora of researchers based on minimizations of twist and curvature and different tiling techniques. One-to-many problem is the one in which at least one plane must have more than one contour and have correspondence with the contour at adjacent layers. Many-to-many problem is stated as m contours at i-th layer and n contours at (i+1)th layer. This problem can be solved by combining one-to-many branching methodology. Branching problem is very important in CAD, medical imaging and geographical information system(GIS).

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.2
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• pp.123-134
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• 2000

This paper addresses a new triangulation method for constructing surface model from a set of wire-frame contours. The most important problem of contour triangulation is the branching problem, and we provide a new solution for the double branching problem, which occurs frequently in real data. The multiple branching problem is treated as a set of double branchings and an algorithm based on contour merging is developed. Our double branching algorithm is based on partitioning of root contour by Toussiant's polygon triangulation algorithml[14]. Our double branching algorithm produces quite natural surface model even if the branch contours are very complicate in shape. We treat the multiple branching problem as a problem of coarse section sampling in z-direction, and provide a new multiple branching algorithm which iteratively merge a pair of branch contours using imaginary interpolating contours. Our method is a natural and systematic solution for the general branching problem of contour triangulation. The result shows that our method works well even though there are many complicated branches in the object.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.39
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• pp.9-18
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• 1996

Many algorithms have been developed for optimizing the asymmectric traveling salesman problem known as a representative NP-Complete problem. The most efficient ones of them are branch and bound algorithms based on the subtour elimination approach. To increase efficiency of the branch and bound algorithm. number of decision nodes should be decreased. For this the minimum bound that is more close at the optimal solution should be found or an effective bounding strategy should be used. If the optimal solution has been known, we may apply it usefully to branching. Because a good feasible solution should be found as soon as possible and have similar features of the optimal solution. By the way, the upper bound solution in branch and bound algorithm is most close at the optimal solution. Therefore, the upper bound solution can be used instead of the optimal solution and information of which can be applied to new branching criteria. As mentioned above, this paper will propose an effective branching rule using the information of the upper bound solution in the branch and bound algorithm. And superiority of the new branching rule will be shown by comparing with Bellmore-Malone's one and carpaneto-Toth's one that were already proposed.

• The KIPS Transactions:PartB
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• v.14B no.6
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• pp.413-422
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• 2007

This paper addresses a new technique for constructing surface model from a set of wire-frame contours. The most difficult problem of this technique, called contour triangulation, arises when there are many branches on the surface, and causes lots of ambiguities in surface definition process. In this paper, the branching problem is reduced as the surface reconstruction from a set of virtual belts and virtual canyons. To tile the virtual belts, a divide-and-conquer strategy based tiling technique, called the BPA algorithm, is adopted. The virtual canyons are covered naturally by an iterative convex removal algorithm with addition of a center vertex for each branching surface. Compared with most of the previous works reducing the multiple branching problem into a set of tiling problems between contours, our method can handle the problem more easily by transforming it into more simple topology, the virtual belt and the virtual canyon. Furthermore, the proposed method does not involve any set of complicated criteria, and provides a simple and robust algorithm for surface triangulation. The result shows that our method works well even though there are many complicated branches in the object.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.1
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• pp.77-93
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• 1998

It is discussed how to locate idle vehicles of AGVS on unidirectional guide paths. The problem is modeled as a median location problem on a cyclic network. The characteristics of the optimal location are analyzed and some useful properties are suggested to reduce the solution space. Based on the properties found, several special types of networks - a pure single-loop type, the loop type with a single branching intersection and the loop type with local branching node - are also analyzed as well as the general cyclic network. In each case of the networks, a solution procedure is suggested. Some numerical examples are provided to illustrate the algorithms developed.

• Korean Management Science Review
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• v.26 no.3
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• pp.1-9
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• 2009

In this paper, we present mathematical models for the ring covering problems arising in the design of multi-ring WDM networks. Also, we present efficient algorithms to solve the suggested models. By the computational experiment, our model can solve the medium-sized networks efficiently and shows better performance than the existing heuristic method. Although we propose an efficient method for the column generation procedure, branching rule that does not destroy the column generation structure is unsolved. Further research is required to develop an effective branching rule.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.830-833
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• 2005

SDM(Structural Dynamics Modification) is to improve dynamic characteristics of a structure, more specifically of a base structure, by adding or deleting auxiliary(modifying) structures. In this paper, I will focus on the optimal layout of the stiffeners which are attached to the plate to maximize 1st natural frequency. Recently, a new topology method was proposed by yamazaki. He uses growing and branching tree model. I modified the growing and branching tree model. The method is designated modified tree model. To expand the layout of stiffeners, I will consider non-matching problem. The problem is solved by using local lagrange multiplier without the mesh regeneration. Moreover The CMS(Component mode synthesis) method is employed to reduce the computing time of eigen reanalysis using reduced componet models.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.2
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• pp.1-19
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• 1994

A generalized network problem is a special class of linear programming problem whose coefficient matrix contains at most two nonzero elements per column. A generalized network problem with 0-1 flow restrictions is called an integer generalized network(IGN) problem. In this paper, we presented a branch and bound algorithm for the IGN that uses network relaxation. To improve the procedure, we develop various strategies, each of which employs different node selection criterion and/or branching variable selection criterion. We test these solution strategies and compare their efficiencies with LINDO on 70 randomly generated problems.

• Journal of the Korea Computer Industry Society
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• v.5 no.3
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• pp.377-382
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• 2004

An unconstrained three-dimensional cutting problem describes the process of finding the cutting pattern that yields the maximum total profit-sum for the small parallelepipeds pieces cut from a large parallelepiped box and there is no limit to the number of pieces to be cut. The problem is a classic NP-hard. The bottom-up approach, which generates all of the feasible cutting patterns by combining two other cutting patterns, can be applied to the three-dimensional problem. We introduce a build and new branching strategies for the unconstrained three-dimensional cutting problem. The strategies are all generalized from the branching strategies proposed by G et at. to solve unconstrained two-dimensional cutting problems.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.406-412
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• 2001

IP address lookup is to determine the next hop destination of an incoming packet in the router. The address lookup is a major bottleneck in high performance router due to the increased routing table sizes, increased traffic, higher speed links, and the migration to 128 bits IPv6 addresses. IP lookup time is dependent on data structure of lookup table and search scheme. In this paper, we propose a new approach to build a lookup table that satisfies the memory constraint. The design of lookup table is formulated as an optimization problem. The objective is to minimize average depth from the root node for lookup. We assume that the frequencies with which prefixes are accessed are known and the data structure is level compressed trie with branching factor $\kappa$ at the root and binary at all other nodes. Thus, the problem is to determine the branching factor k at the root node such that the average depth is minimized. A heuristic procedure is proposed to solve the problem. Experimental results show that the lookup table based on the proposed heuristic has better average and the worst-case depth for lookup.