• Journal of KIISE:Software and Applications
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• v.29 no.1_2
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• pp.20-29
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• 2002

The composite stock cutting problem is to allocate rectangular and/or irregular patterns onto a large composite stock sheet of finite dimensions in such a way that the resulting scrap will be minimized. In this paper, the distributed simulated annealing with the new cost error tolerant spatial decomposition is applied to the composite stock cutting problem in MPI environments. The cost error tolerant scheme relaxes synchronization and chooses small perturbations on states asynchronously in a dynamically changed stream length to keep the convergence property of the sequential annealing. This paper proposes the efficient data structures for representation of patterns and their affinity relations and also shows how to determine move generations, annealing parameters, and a cost function. The spatial decomposition method is addressed in detail. This paper identifies that the final quality is not degraded with almost linear speedup. Composite stock shapes are not constrained to convex polygons or even regular shapes, but the rotations are only allowed to 2 or 4 due to its composite nature.

• Journal of the Korea Society of Computer and Information
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• v.20 no.1
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• pp.85-92
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• 2015

As computer game maps get more elaborate, path-finding by using $A^*$ algorithm in grid-based game maps becomes bottlenecks of the overall game performance. It is because the search space becomes large as the number of nodes increases with detailed representation in cells. In this paper we propose an efficient pathfinding method in which the computer game maps in a regular grid is converted into the polygon-based representation of the list of vertices and then the visibility information about vertices of polygons can be utilized. The conversion to the polygon-based map does not give any effect to the real-time query process because it is preprocessed offline. The number of visited nodes during search can be reduced dramatically by designing heuristics using visibility information of vertices that make the accuracy of the estimation enhanced. Through simulations, we show that the proposed methods reduce the search space and the search time effectively while maintaining the advantages of the grid-based method.

• Journal of the Korean School Mathematics Society
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• v.20 no.1
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• pp.43-56
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• 2017

In this thesis, the extension of the pyramid is contemplated through the pyramids presented in textbook $\ll$Math 6-1${\gg}$ published according to the 2009 revised curriculum. In textbook $\ll$Math 6-1${\gg}$, the pyramid is defined by presenting rough sketches of typical pyramids in an extensional definition method. This contrasts with the method of defining the pyramid by using such an extensional definition and a connotative definition method that reveals common properties of all pyramids. In textbook $\ll$Math 6-1${\gg}$, right pyramids whose base can not be regarded as regular polygons, and oblique pyramids are hardly presented. Nonetheless, $\ll$Math 6-1 Teacher's Guide Book${\gg}$ says that we have no choice but to handle oblique pyramids. In this thesis, based on these results, the following implications are presented as conclusions. First, there should be enough discussion on the extension of the pyramid in elementary school mathematics, and agreement to the results. In particular, such discussions are highly necessary in revising the curriculum. Second, in the process of realizing the intention of the curriculum in the textbook through the teacher's guidebook, the extension of the pyramid must be consistent. Third, there should be some consensus about the knowledge that elementary teachers should know about the pyramid.