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The dotted line in red represents a cut with three crossing edges. The dashed line in green represents one of the minimum cuts of this graph, crossing only two edges. [1] In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric.
Minimization is done using a standard minimum cut algorithm. Due to the max-flow min-cut theorem we can solve energy minimization by maximizing the flow over the network. The max-flow problem consists of a directed graph with edges labeled with capacities, and there are two distinct nodes: the source and the sink. Intuitively, it is easy to see ...
A min-cut of a weighted graph having min-cut weight 4 [1] In graph theory, the Stoer–Wagner algorithm is a recursive algorithm to solve the minimum cut problem in undirected weighted graphs with non-negative weights. It was proposed by Mechthild Stoer and Frank Wagner in 1995.
A graph and two of its cuts. The dotted line in red is a cut with three crossing edges. The dashed line in green is a min-cut of this graph, crossing only two edges. In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David Karger and first ...
The illustration on the right shows a minimum cut: the size of this cut is 2, and there is no cut of size 1 because the graph is bridgeless. The max-flow min-cut theorem proves that the maximum network flow and the sum of the cut-edge weights of any minimum cut that separates the source and the sink are equal. There are polynomial-time methods ...
In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the total weight of the edges in a minimum cut, i.e., the smallest total weight of the edges which if removed would disconnect the source from the sink.
Graph cut optimization is a combinatorial optimization method applicable to a family of functions of discrete variables, named after the concept of cut in the theory of flow networks. Thanks to the max-flow min-cut theorem , determining the minimum cut over a graph representing a flow network is equivalent to computing the maximum flow over the ...
In combinatorial optimization, the Gomory–Hu tree [1] of an undirected graph with capacities is a weighted tree that represents the minimum s-t cuts for all s-t pairs in the graph. The Gomory–Hu tree can be constructed in | V | − 1 maximum flow computations. It is named for Ralph E. Gomory and T. C. Hu.