• 대한산업공학회지
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• 제23권2호
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• pp.359-370
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• 1997

We consider a facility layout problem with the objective of minimizing total transportation distance, which is the sum of rectilinear distances between facilities weighted by the frequency of trips between the facilities. It is assumed that facilities are required to have rectangular shapes and there is no empty space between the facilities in the layout. In this study, a graph theoretic heuristic is developed for the problem. In the heuristic, planar graphs are constructed to represent adjacencies between the facilities and then the graphs are converted to block layouts on a continual plane using a layout construction module. (Therefore, each graph corresponds to a layout.) An initial layout is obtained by constructing a maximal weighted planar graph and then the layout is improved by changing the planar graph. A simulated annealing algorithm is used to find a planar graph which gives the best layout. To show the performance of the proposed heuristic, computational experiments are done on randomly generated test problems and results are reported.

• 농촌계획
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• 제6권2호
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• pp.12-19
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• 2000

Irrigation pipeline networks consist mainly of buried pipes and are therefore relatively free from topographic constraints. Installation of irrigation pipeline systems is increasing since the systems have several advantages compared to open channel systems. To achieve economic design of pipeline networks, the layout should meet several conditions such as shortest path, maximum flow, and least cost. Graph theory is mathematical tool which enable to find out optimum layout for complicated network systems. In this study, applicability of graph theory to figure out optimum layout of irrigation pipeline networks was evaluated.

• Genomics & Informatics
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• 제6권3호
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• pp.147-152
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• 2008

The basic graph layout technique, one of many visualization techniques, deals with the problem of positioning vertices in a way to maximize some measure of desirability in a graph. The technique is becoming critically important for further development of the field of systems biology. However, applying the appropriate automatic graph layout techniques to the genomic scale flow of metabolism requires an understanding of the characteristics and patterns of duplicate and shared vertices, which is crucial for bioinformatics software developers. In this paper, we provide the results of parsing KEGG XML files from a graph-theoretical perspective, for future research in the area of automatic layout techniques in biological pathway domains.

• 대한전자공학회논문지
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• 제23권2호
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• pp.217-224
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• 1986

In case of VLSI design, the shuffle-exchange graph is useful for optimal layout. HOEY and LEISERSON proposed the method of drawing a N-nodes shuffle-exchange graph on O(N2/log N) layout area by using the complex plane digram. [2] In this paper, a new algorithm for drawing the shuffle-exchange graph is proposed. This algorithm is not by using the complex plane diabram, but the table of e decimal represented nodes of shuffle-edge relations. And the structural properties for optimal layout of the graph are summarized and verified. By using this more simplified algorithm, a FORTRAN program which can be treated faster is written. Aimed near optimal shuffle-exchange graphs are printed out by giving inputs` the number of nodes.

• 한국CDE학회논문집
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• 제6권3호
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• pp.174-183
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• 2001

This study proposes an improved genetic algorithm (GA) to derive solutions for facility layout problems having inner walls and passages. The proposed algorithm models the layout of facilities on a flour-segmented chromosome. Improved solutions are produced by employing genetic operations known as selection, crossover, inversion, mutation, and refinement of these genes for successive generations. All relationships between the facilities and passages are represented as an adjacency graph. The shortest path and distance between two facilities are calculated using Dijkstra's algorithm of graph theory. Comparative testing shows that the proposed algorithm performs better than other existing algorithm for the optimal facility layout design. Finally, the proposed algorithm is applied to ship compartment layout problems with the computational results compared to an actual ship compartment layout.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.209-224
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• 2006

This paper presents an optimization model with performance constraints for two kinds of graph elements layout problem. The layout problem is partitioned into finite subproblems by using graph theory and group theory, such that each subproblem overcomes its on-off nature about optimal variable. Furthermore each subproblem is relaxed and the continuity about optimal variable doesn't change. We construct a min-max problem which is locally equivalent to the relaxed subproblem and develop the first order necessary and sufficient conditions for the relaxed subproblem by virtue of the min-max problem and the theories of convex analysis and nonsmooth optimization. The global optimal solution can be obtained through the first order optimality conditions.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.283-290
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• 2008

This paper is motivated by the problem of fitting a group of cuboids into a simplified rotating vessel of the artificial satellite. Here we introduce a combinatorial optimization model which reduces the three-dimensional layout problem with behavioral constraints to a finite enumeration scheme. Moreover, a global combinatorial optimization algorithm is described in detail, which is an improved graph-theoretic heuristic.

• 한국정보과학회논문지:소프트웨어및응용
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• 제36권11호
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• pp.875-890
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• 2009

대사체학은 대사 경로 네트워크를 통해 생명 활동을 이해하고자 하는 분야로서, 대사 경로 내의 흐름을 한 눈에 알 수 있도록 가시화하여 보여 주는 도구가 반드시 필요하다. 이러한 가시화 도구의 경우 노드수가 증가할수록 에지 교차가 기하급수적으로 증가하는 문제가 있다. 따라서 유전체 수준의 대사경로를 연구하기 위해서는 대사 경로 그래프 레이아웃 상에 나타나는 에지 교차를 줄이는 것이 시각화의 매우 중요한 부분이다. 본 논문에서는 대사 경로의 구조적인 특징에 기반한 3차원 공간 상에 대사 경로 그래프를 레이아웃해 주는 모듈을 설계, 구현하였다. 2-계층 레이아웃을 이용하여 대사 경로 그래프를 계층적으로 레이아웃함으로써 표현영역을, 3차원으로 확장시키고 기존의 2차원 레이아웃 알고리즘 적용시 번번히 나타나는 에지 교차의 수를 감소시키는 결과를 얻었다.

• 대한전자공학회논문지
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• 제19권6호
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• pp.62-66
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• 1982

LSI의 레이아웃 CAD 시스템에 있어서 미체선 신호면에 대한 초선가능성을 판정하고 그것을 수정·해결하는 것은 중요하다. 본 논문에서는 무향 그라프 G=(V, E)를 도입하여 2개의 절점 독립(vertex-disjoint)경로의 존재여부를 판정하는 알고리즘을 제안하고, 경로가 존재하는 경우는미결선 신호선을 해결하고, 존재하지 않는 경우는 해결할 수 없음을 보이는 방법을 제시하였다. 제안한 알고리즘의 시간 복잡도는 O(|VlxlEl)이다. A method finding out routability for unrouted signal lines and rerouting those which are turned out to be able to route in layout design of LSI is described. In this paper the problems of finding two-disjoint Paths represented by an undirected graph G=(V,E), where V,E are sets of vertices and edges respectively, are studied. The existence of two-disjoint paths from s1, to t1, (called P1) and from S2 to T2 (called P2) indicated by the four vertices on the graph s1, t1, s2, t2 ∈ V means that two distinct signal lines exist in layout design. It turns out that the proposed time complexity in the algorithm is O (IVI x IEI).

• 반도체디스플레이기술학회지
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• 제9권2호
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• pp.15-20
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• 2010

This paper deals with minimizing layout area of FPGA design. FPGAs are becoming increasingly important in the design of ASICs since they provide both large scale integration and user-programmability. This paper describes a method to obtain tight bound on the worst-case increase in area when drivers are introduced along many long wires in a layout. The area occupied by minimum-area embedding for a circuit can depend on the aspect ratio of the bounding rectangle of the layout. This paper presents a separator-based area-optimal embeddings for FPGA graphs in rectangles of several aspect ratios which solves the longest path problem in the constraint graph.