• 대한산업공학회지
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• 제27권3호
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• pp.250-259
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• 2001

Given a tree structured network in which each node has its own demand and also stands for a candidate location of a potential facility, such as plant or warehouse, a capacitated facility location problem on the network (CFLPOT) is to decide capacitated facility locations so that the total demand occurred on the network can be satisfied from those facilities with the minimum cost. In this paper, we first introduce a mixed integer programming formulation for CFLPOT with two additional assumptions, the indivisible demand assumption and the contiguity assumption and then show that it can be reformulated as a tree partitioning problem with an exponential number of variables. We then show that it can be solved in O($n^2b$) time by utilizing the limited column generation method developed by Shaw (1993), where n is the total number of nodes in the network and b is the maximum facility capacity. We also develop a depth-first dynamic programming algorithm with a running time of O(nb) for finding the locally maximal reduced cost which plays an important role in the limited column generation method. Finally, we implement our algorithms on a set of randomly generated problems and report the computational results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권10호
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• pp.5244-5259
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• 2019

With the continuous development of LBS (Location Based Service) applications, privacy protection has become an urgent problem to be solved. Differential privacy technology is based on strict mathematical theory that provides strong privacy guarantees where it supposes that the attacker has the worst-case background knowledge and that knowledge has been applied to different research directions such as data query, release, and mining. The difficulty of this research is how to ensure data availability while protecting privacy. Spatial multidimensional data are usually released by partitioning the domain into disjointed subsets, then generating a hierarchical index. The traditional data-dependent partition methods need to allocate a part of the privacy budgets for the partitioning process and split the budget among all the steps, which is inefficient. To address such issues, a novel two-step partition algorithm is proposed. First, we partition the original dataset into fixed grids, inject noise and synthesize a dataset according to the noisy count. Second, we perform IH-Tree (Improved H-Tree) partition on the synthetic dataset and use the resulting partition keys to split the original dataset. The algorithm can save the privacy budget allocated to the partitioning process and obtain a more accurate release. The algorithm has been tested on three real-world datasets and compares the accuracy with the state-of-the-art algorithms. The experimental results show that the relative errors of the range query are considerably reduced, especially on the large scale dataset.

• 전자공학회논문지C
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• 제34C권2호
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• pp.38-49
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• 1997

In this paper, w describe partitioning large circuits into multiple chips on the programmable FPCB for rapid prototyping. FPCBs consists of areas for FPGAs for logic and interconnect components, and the routing topology among them are predetermined. In the partition problem for FPCBs, the number of wires ofr routing among chips is fixed, which is an additonal constraints to the conventional partition problem. In order to deal with such aconstraint properly we first define a new partition problem, so called the topologybased partition problem, and then propose a heuristic method. The heuristic method is based on the simulated annealing and clustering technique. The multi-level tree clustering technique is used to obtain faster and better prtition results. In the experimental results for several test circuits, the restrictions for FPCB were all satisfied and the needed execution time was about twice the modified K-way partition method for large circuits.

• 대한산업공학회지
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• 제27권4호
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• pp.394-405
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• 2001

Since most real-world application data involve continuous-valued attributes, properly addressing the discretization process for constructing a decision tree is an important problem. A continuous-valued attribute is typically discretized during decision tree generation by partitioning its range into two intervals recursively. In this paper, by removing the restriction to the binary discretization, we present a hybrid multi-interval discretization algorithm for discretizing the range of continuous-valued attribute into multiple intervals. On the basis of experiment using semiconductor etching machine, it has been verified that our discretization algorithm constructs a more efficient incremental decision tree compared to previously proposed discretization algorithms.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 ISIS 2003
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• pp.330-333
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• 2003

Initial cluster size for clustering of partitioning methods is very important to the clustering result. In K-means algorithm, the result of cluster analysis becomes different with optimal cluster size K. Usually, the initial cluster size is determined by prior and subjective information. Sometimes this may not be optimal. Now, more objective method is needed to solve this problem. In our research, we propose a hybrid genetic algorithm, a tree induction based evolution algorithm, for determination of optimal cluster size. Initial population of this algorithm is determined by the number of terminal nodes of tree induction. From the initial population based on decision tree, our optimal cluster size is generated. The fitness function of ours is defined an inverse of dissimilarity measure. And the bagging approach is used for saying computational time cost.

• 전자공학회논문지A
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• 제33A권11호
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• pp.128-139
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• 1996

In this paper, we propose an algorithm to solve the problem of placement of rectangular blocks whose sizes and shpaes are pre-determined. The proposed method solves the placement of many retangular blocks of different sizes and shapes in a hierarchical manner, so as to minimize the chip area. The placement problem is divided into several sub-problems: hierarchical partioning, hierarchical area/shape estimation, hierarchical pattern pacement, overlap removal, and module rotation. After the circuit is recursively partitioned to build a hierarchy tree, the necessary wiring area and module shpaes are estimated using the resutls of the partitioning and the pin information before the placement is performed. The placement templaes are defined to represent the relative positions of the modules. The area and the connectivity are optimized separately at each level of hierachy using the placement templates, so the minimization of chip area and wire length can be achieved in a short execution time. Experiments are made on the MCNC building block benchmark circuits and the results are compared with those of other published methods. The proposed technique is shown to produce good figures in tems of execution time and chip area.

• 한국컴퓨터정보학회논문지
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• 제3권4호
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• pp.63-69
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• 1998

전력분배 네트워크의 면적 최적화는 VLSI 시스템의 레이아웃 디자인에 중요한 문제이다. 본 논문에서는 전압 하강과 전기 이동 제약을 만족하는 전력분배 네트의 최소 면적을 디자인 하기위해 문제를 해결하는 새로운 방법을 제안한다. 전력 네트 디자인에 대한두가지의 새로운 greedy heuristics을 제안했는데 하나는 bottorm-up 트리 구조와 다른 하나는 top-down 분리 분할 기법을 기본으로 한 것이다.

• 한국경영과학회지
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• 제23권2호
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• pp.29-46
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• 1998

In this paper, we develop detailed algorithms for implementing the so-called Limited Column Generation procedure for Local Access Telecommunication Network(LATN) design problem. We formulate the problem into a tree-partitioning problem with an exponential number of variables. Its linear programming relaxation has all integral vertices, and can be solved by the Limited Column Generation procedure in just n pivots, where n is the number of nodes in the network. Prior to each pivot. an entering variable is selected by detecting the Locally Most Violated(LMV) reduced cost, which can be obtained by solving a subproblem in pseudo-polynomial time. A critical step in the Limited Column Generation is to find all the LMV reduced costs. As dual variables are updated at each pivot, the reduced costs have to be computed in an on-line fashion. An efficient implementation is developed to execute such a task so that the LATN design problem can be solved in O(n$^2$H), where H is the maximum concentrator capacity. Our computational experiments indicate that our algorithm delivers an outstanding performance. For instance, the LATN design problem with n＝150 and H＝1000 can be solved in approximately 67 seconds on a SUN SPARC 1000 workstation.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1995년도 춘계공동학술대회논문집; 전남대학교; 28-29 Apr. 1995
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• pp.54-68
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• 1995

In this paper, we develop detailed algorithms for implementing the so-called Limited Column Generation procedure for Local Access Telecommunication Network (LATN) Design problem. We formulate the problem into a tree-partitioning problem with an exponential number of variables. Its linear programming relaxation has all integral vertices, and can be solved by the Limited Column. Generation procedure in just n pivots, where n is the number of nodes in the network. Prior to each pivot, an entering variable is selected by detecting the Locally Most Violated (LMV) reduced cost, which can be obtained by solving a subproblem in pseudo-polynomial time. A critical step in the Limited Column Generation is to find all the LMV reduced costs. As dual variables are updated at each pivot, the reduced costs have to be computed in an on-line fashion. An efficient implementation is developed to execute such a task so that the LATN Design problem can be solved in O(n$^{2}$H), where H is the maximum concentrator capacity. Our computational experiments indicate that our algorithm delivers an outstanding performance. For instance, the LATN Design problem with n = 150 and H = 1000 can be solved in approximately 67 seconds on a SUN SPARC 1000 workstation.

• 한국컴퓨터그래픽스학회논문지
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• 제5권2호
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• pp.9-23
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• 1999

가시성 전처리는 렌더링을 위하여 실시간에 처리되어야 하는 다각형의 수를 줄여, 전체 랜더링 성능을 향상시키는 유용한 방법 중에 하나이다. 본 논문에서는 새롭고 효율적인 가시성 전처리 방법을 제안하였다. 제안된 방법에서는 가상환경 내에서 네비게이션 가능한 지역들이 사전에 직육면체 형태의 셀들로 분할되어 있다고 가정한다. 분할된 하나의 셀에서 보일 가능성이 있는 다각형을 구하기 위해서는 적어도 면-대-면 가시성을 해결해야 한다. 이는 4차원의 가시성 정보를 다루어야 함을 의미한다. 제안된 방법에서는 이러한 4차원이라는 고차원의 가시성 정보를 보다 효율적으로 처리하기 위해서, 포괄적 가시성의 특성을 이용하여 4차원의 정보를 2차원의 평면들에 나타내고 이를 개념적으로 2진공간분할(Binary Space Partitioning) 트리와 유사한 3진트리로 표현하여 처리하였다. 제안된 방법은 건축물 내부환경뿐만 아니라, 도시환경과 같은 보다 일반적인 야외환경도 다룰 수 있으며, 여러 개의 다각형들이 협력적으로 가리는 다각형들도 제거할 수 있다. 제안된 방법은 O(nm)의 계산 시간과 O(n+m)의 공간을 요구한다. 적당한 m을 선택함으로써 사용자는 전처리시간과 계산결과사이에 적절한 선택을 할 수 있다.