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Open image in new window Fig. 3 Example of minimum cut in IEEE 9-bus system.
Scaling laws for the behavior of the shortest path and minimum cut in random networks are then surveyed.
Then a global minimum cut in undirected graph equals to the minimum value from the two parts.
The Stoer-Wagner method [31] is an efficient algorithm for seeking global minimum cut in an undirected graph G = (V, E).
In the first stage, the CISG is obtained rapidly by achieving the minimum cut in the generator dynamic connection graph using Stoer-Wagner algorithm.
In this paper, we present the fastest algorithm known today for computing a minimum cut in a hypergraph which is a non-trivial extension of the result in Stoer and Wagner (J. ACM 44 (4) (1997) 586).
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The methods based on minimum cuts in a graph are designed to minimize the similarity between pixels that are being split [22, 23, 26].
In "Shortest paths in correlated networks" and "Minimum cuts in correlated networks" sections, we study the shortest path problem and min-cut problem, respectively, for the proposed models and devise algorithms to solve them exactly.
Recently, two very fast algorithms for computing minimum cuts in graphs were reported (Nagamochi and Ibaraki; SIAM J. Discrete Math. 5 (19921992) 54; Stoer and Wagner, J. ACM 44 (4) (1997) 585).
Consequently, based on these link weight assignments, the MC-NSRLG problem in Fig. 8 can be reduced to the SP-SRLG problem in Fig. 7, similar to the proof of the MCDCM problem in "Minimum cuts in correlated networks" section.
Similar to the proof that the MCDCM problem is NP-hard in "Minimum cuts in correlated networks" section, the MC-SRLG problem in the form of Fig. 6 can be reduced to the NP-hard SP-SRLG problem.
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