• 한국인터넷방송통신학회논문지
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• 제13권1호
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• pp.143-152
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• 2013

주어진 그래프 G=(V,E), n=|V|, m=|E|에 대해 최소절단을 찾는 연구는 공급처 s와 수요처 t가 주어지지 않은 경우와 주어진 경우로 구분된다. s와 t가 주어지지 않은 무방향 가중 그래프에 대한 Stoer-Wagner 알고리즘은 임의의 정점을 고정시키고 최대 인접 순서로 나열하여 마지막 정점의 절단 값과 마지막 2개 정점을 병합하면서 정점을 축소시키는 방법으로 $\frac{n(n-1)}{2}$회를 수행한다. 또한, s와 t가 주어진 그래프에 대한 Ford-Fulkerson 알고리즘은 증대경로를 탐색하여 절단 간선을 결정한다. 더 이상의 증대 경로가 없으면 절단 간선들의 조합으로 최소절단을 결정해야 한다. 본 논문은 단일 s와 t가 주어진 무방향 가중 그래프에 대해 최대인접 병합과 절단값을 동시에 계산하는 방법으로 n-1회 수행으로 단축시켰다. 또한, Stoer-Wagner 알고리즘은 최소 절단을 기준으로 V=S+T로 양분하지 못할 수 있는데 반해 제안된 알고리즘은 정확히 양분시켰다. 제안된 알고리즘은 Ford-Fulkerson의 증대경로를 찾는 수행횟수보다 많이 수행하지만 수행과정에서 최소절단을 결정하는 장점이 있다.

• 한국인터넷방송통신학회논문지
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• 제12권5호
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• pp.129-139
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• 2012

공급처 s와 수요처 t, 호가 수용량을 갖고 있는 방향 그래프 망 $D=(N,A),n{\in}N,a=c(u,v){\in}A$에 대해, 공급처 s에서 수요처 t로의 최대 흐름양은 N을 $s{\in}S$와 $t{\in}T$의 집합으로 분리시키는 최소절단값이 결정한다. 최소절단을 찾는 대표적인 알고리즘으로는 수행복잡도 $O(NA^2)$의 Ford-Fulkerson이 있다. 이 알고리즘은 가능한 모든 증대경로를 탐색하여 병목지점을 결정한다. 알고리즘이 종료되면 병목지점들의 조합으로 N=S+T의 절단이 되는 최소 절단을 결정해야 한다. 본 논문은 S={s}, T={t}를 초기값으로 설정하고, 망의 최대 수용량 호 $_{max}c(u,v)$를 인접한 S나 T로 병합시키고 절단값을 구하는 최대인접병합 알고리즘을 제안하였다. 최대인접병합 알고리즘은 n-1회를 수행하지만 알고리즘 수행 과정에서 최소절단을 찾는 장점을 갖고 있다. Ford-Fulkerson과 최대인접병합 알고리즘을 다양한 8개의 방향 그래프에 적용한 결과 제안된 알고리즘은 수행복잡도 O(N)인 n-1회 수행 과정에서 최소절단을 쉽게 찾을 수 있었다.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.77-86
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• 2002

Ford and Fulkerson have shown that a stationary maximal dynamic flow can be obtained by solving a transhipment problem associated with the static network and thereby finding the maximal temporally repeated dynamic flow. This flow is known to be an optical dynamic flow. This paper presents an algorithm for second best temporal1y repeated flows. A numerical example is presented.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 추계학술대회 논문집 전력기술부문
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• pp.261-265
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• 2004

This paper proposes a fuzzy dual method for analyzing long-term transmission system expansion planning problem considering ambiguities of the power system using fuzzy lineal programming. Transmission expansion planning problem can be formulated integer programming or linear programming with minimization total cost subject to reliability (load balance). A long-term expansion planning problem of a grid is very complex, which have uncertainties fur budget, reliability criteria and construction time. Too much computation time is asked for actual system. Fuzzy set theory can be used efficiently in order to consider ambiguity of the investment budget (economics) for constructing the new transmission lines and the delivery marginal rate (reliability criteria) of the system in this paper. This paper presents formulation of fuzzy dual method as first step for developing a fuzzy Ford-Fulkerson algorithm in future and demonstrates sample study. In application study, firstly, a case study using fuzzy integer programming with branch and bound method is presented for practical system. Secondly, the other case study with crisp Ford Fulkerson is presented.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.379-389
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• 2000

FORD and FULKERSON have shown that a stationary maximal dynamic flow can be obtained by solving a transhipment problem associated with the static network and thereby finding the maximal temporally repeated dynamic flow. This flow is known to be an optimal dynamic flow. this paper presents the remark that temporally repeated flows may be not optimal for a minimal dynamic flow and an algorithm for such a flow. a numerical example is presented.

• 대한교통학회지
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• 제8권2호
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• pp.67-75
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• 1990

This paper treats the problem to schedule for trains with how transit priority so as to maximizing the number that can be sent during given time periods without interfering with the fixed schedule for train with high transit priority in a track. We transform the this problem into Time Expanded Network without traverse time through application of Ford and Fulkerson Model and construct the Enumeration Algorithm for solutions using TENET Generator (TENETGEN). Finally, we compare our algorithm with Dinic's Maximal-Flow Algorithm and examine the avaliability of our procedures in personal computer.

• 산업경영시스템학회지
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• 제13권21호
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• pp.111-117
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• 1990

This paper treats the problem to schedule for train with low transit priority so as to maximizing the number that can be sent during given time without interfering with the fixed schedule for train with high transit priority in a track. We transform the this problem into Time-Expanded Network without traverse time through application of Ford-Fulkerson Model, develop a TENET GENerator(TENETGEN) and obtain the data of TENET using developed TENETGEN. Finally, we seek the optimal solution to these data with Dinic's Maximal-Flow Algorithm and examine the availability of our procedures in personal computer.

• 한국정밀공학회지
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• 제26권2호
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• pp.141-147
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• 2009

We introduce a noble method to find a variation of the optimal path problem. The problem is to find the optimal decomposition of an original planar region such that the number of paths in the region is minimized. The paths are required to uniformly cover each subregion and the directions of the paths in each sub-region are required to be either entirely vertical or entirely horizontal. We show how we can transform the path problem into a graph s-t cut problem. We solve the transformed s-t cut problem using the Ford-Fulkerson method and show its performance. The approach can be used in zig-zag milling and layerd manufacturing.

• 한국국방경영분석학회지
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• 제2권1호
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• pp.145-162
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• 1976

For a large organization such as a military service which can foresee future growths in its manpower requirements, a systematic tool that can provide analysis of its present manpower structure and policies in terms of meeting the future requirements, is in order today. This paper proposes a network model for such a purpose. The ROK Navy officer corps manpower system is studied and formulated as a network model, which may be expressed as a linear programming problem of minimizing total cost. An appropriate cost concept is developed and the out-of-kilter algorithm of Ford and Fulkerson is computer programmed to be used as a solution procedure for this network problem. A case study is conducted with a set of hypothetical data on a possible Navy combat-line specialty manpower problem.

• 산업공학
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• 제4권2호
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• pp.25-34
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• 1991

The problem of scheduling the passage things with low transit priority to maximize the amonnt that can be sent during given time periods without interfering with the fixed schedule for passage things with high transit priority in a track, is treated in this paper. The problem is transformed into the Time Expanded Network without traverse time through the Ford and Fulkerson Model and the Enumeration Algorithm is developed for solutions using TENET GENerator(TENETGEN). Finally, the proposed algorithm is compared with Dinic's maximal-flow algorithm and examined for the availability of the procedures on the personal computer.