• Journal of the Korea Society of Computer and Information
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• v.21 no.6
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• pp.77-81
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• 2016

This paper deals with the optimization problem that decides the routing of connection between multi-source and multi-sink. For this problem, there is only in used the mathematical approach as linear programming (LP) software package and has been unknown the polynomial time algorithm. In this paper we suggest the heuristic algorithm with $O(mn)^2$ time complexity to solve the optimal solution for this problem. This paper suggests the simple method that assigns the possible call flow quantity to augmenting path of ($s_i,t_i$) city pair satisfied with demand of ($s_i,t_i$). The proposed algorithm can be get the same optimal solution as LP for experimental data.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.845-851
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• 2002

An efficient method is developed to obtain the maximum flow for a network when its simple paths are known. Most of the existing techniques need to convert simple paths into minimal cuts, or to determine the order of simple paths to be applied in the process to reach the correct result. In this paper, we propose a method based on the concepts of signed simple path and signed flow defined in the text. Our method involves a fewer number of arithmetic operations at each iteration, and requires fewer iterations in the whole process than the existing methods. Our method can be easily extended to a mixed network with a slight modification. Furthermore, the correctness of our method does not depend on the order of simple paths to be applied in the process.

• Proceedings of the Korean Reliability Society Conference
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• 2002.06a
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• pp.297-302
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• 2002

An efficient method is developed to obtain the maximum capacity flow for a network when its simple paths are known. Most of the existing techniques need to convert simple paths into minimal cuts, or to determine the order of simple paths to be applied in the process to reach the correct result. In this paper, we propose a method based on the concepts of signed simple path and signed flow defined in the text. Our method involves a fewer number of arithmetic operations at each iteration, and requires fewer iterations in the whole process than the existing methods. Our method can be easily extended to a mixed network with a slight modification. Furthermore, the correctness of our method does not depend on the order of simple paths to be applied in the process.

• Proceedings of the Korean Reliability Society Conference
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• 2001.06a
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• pp.455-462
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• 2001

We propose a new method to evaluate the network reliability which greatly reduces the intermediate steps toward calculations of maximum capacity flow by excluding unnecessary simple paths contained in the set of failure simple paths. By using signed simple paths and signed flow, we show that our method is more efficient than that of Lee and Park (2001a) in the number of generated composite paths and in the procedure for obtaining minimal success composite paths. Numerical examples are given to illustrate the use and the efficiency of the method.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.136-145
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• 1993

This paper considers a reliability problem as a special type of flow problem and presents an algorithm to evaluate the exact 2-terminal reliability of networks by using a backtracking technique. It employs a polygon-to-chain reduction in addition to series and parallel reduction techniques to reduce execution time. In comparisons, it presents a much better performance than other algorithms known to us. We also propose a methodology to apply the algorithm for approximation of the system reliability.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.2
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• pp.13-29
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• 1997

This paper considers a new routing problem, successive max-min connection ratio problem (SMCRP), arised in circuit telecommunication networks such as SONET and WDM optical transport network. An optimization model for SMCRP is established based on link-flow formulation. It's first optimization process is an integral version of maximum concurrent flow problem. Integer condition does not give the same connection-ratio of each node-pair at an optimal solution any more. It is also an integral multi-commodity flow problem with fairness restriction. In order to guarantee fairness to every node-pair the minimum of connection ratios to demand is maximized. NP- hardness of SMCRP is proved and a heuristic algorithm with polynomial-time bound is developed for the problem. Augmenting path and rerouting flow are used for the algorithm. The heuristic algorithm is implemented and tested for networks of different sizes. The results are compared with those given by GAMS/OSL, a popular commercial solver for integer programming problem.n among ferrite-pearlite matrix, the increase in spheroidal ratio with increasing fatigue limitation, 90% had the highest, 14.3% increasing more then 70%, distribution range of fatigue.
ife was small in same stress level. (2) $\sqrt{area}_{max}$ of graphite can be used to predict fatigue limit of Ductile Cast Iron. The Statistical distribution of extreme values of $\sqrt{area}_{max}$ may be used as a guideline for the control of inclusion size in the steelmaking.

• 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.19 no.4
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• pp.27-33
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• 2019

The min-cut problem that decides the maximum flow in a complex network flows from source(s) to sink(t) is known as a hard problem. The augmenting path algorithm divides into single path and decides the bottleneck point(edge), but the min-cut section to be decide additionally. This paper suggests O(n) time complexity heuristic greedy algorithm for the number of vertices n that applies free agent system in a pro-sports field. The free agent method assumes $N_G(S),N_G(T)$vertices among $v{\in}V{\backslash}\{s,t\}$to free agent players, and this players transfer into the team that suggest more annual income. As a result of various networks, this algorithm can be finds all of min-cut sections and min-cut value for whole cases.

• 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).