• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.1
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• pp.143-152
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• 2013

Given weighted graph G=(V,E), n=|V|, m=|E|, the minimum cut problem is classified with source s and sink t or without s and t. Given undirected weighted graph without s and t, Stoer-Wagner algorithm is most popular. This algorithm fixes arbitrary vertex, and arranges maximum adjacency (MA)-ordering. In the last, the sum of weights of the incident edges for last ordered vertex is computed by cut value, and the last 2 vertices are merged. Therefore, this algorithm runs $\frac{n(n-1)}{2}$ times. Given graph with s and t, Ford-Fulkerson algorithm determines the bottleneck edges in the arbitrary augmenting path from s to t. If the augmenting path is no more exist, we determine the minimum cut value by combine the all of the bottleneck edges. This paper suggests minimum cut algorithm for undirected weighted graph with s and t. This algorithm suggests MA-merging and computes cut value simultaneously. This algorithm runs n-1 times and successfully divides V into disjoint S and V sets on the basis of minimum cut, but the Stoer-Wagner is fails sometimes. The proposed algorithm runs more than Ford-Fulkerson algorithm, but finds the minimum cut value within n-1 processing times.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.5
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• pp.129-139
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• 2012

Given digraph network $D=(N,A),n{\in}N,a=c(u,v){\in}A$ with source s and sink t, the maximum flow from s to t is determined by cut (S, T) that splits N to $s{\in}S$ and $t{\in}T$ disjoint sets with minimum cut value. The Ford-Fulkerson (F-F) algorithm with time complexity $O(NA^2)$ has been well known to this problem. The F-F algorithm finds all possible augmenting paths from s to t with residual capacity arcs and determines bottleneck arc that has a minimum residual capacity among the paths. After completion of algorithm, you should be determine the minimum cut by combination of bottleneck arcs. This paper suggests maximum adjacency merging and compute cut value method is called by MA-merging algorithm. We start the initial value to S={s}, T={t}, Then we select the maximum capacity $_{max}c(u,v)$ in the graph and merge to adjacent set S or T. Finally, we compute cut value of S or T. This algorithm runs n-1 times. We experiment Ford-Fulkerson and MA-merging algorithm for various 8 digraph. As a results, MA-merging algorithm can be finds minimum cut during the n-1 running times with time complexity O(N).

• Journal of applied mathematics & informatics
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• v.9 no.1
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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.

• Proceedings of the KIEE Conference
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• 2004.11b
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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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• v.7 no.2
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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.

• Journal of Korean Society of Transportation
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• v.8 no.2
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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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.13 no.21
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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.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.2
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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.

• Journal of the military operations research society of Korea
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• v.2 no.1
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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.

• IE interfaces
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• v.4 no.2
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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.