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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 minimum cut problem in undirected, weighted graphs limited to non-negative weights can be solved in polynomial time by the Stoer-Wagner algorithm. In the special case when the graph is unweighted, Karger's algorithm provides an efficient randomized method for finding the cut. In this case, the minimum cut equals the edge connectivity of the ...
He is responsible for Karger's algorithm, a Monte Carlo method to compute the minimum cut of a connected graph. [4] Karger developed the fastest minimum spanning tree algorithm to date, with Philip Klein and Robert Tarjan. They found a linear time randomized algorithm based on a combination of Borůvka's algorithm and the reverse-delete ...
Pages in category "Graph algorithms" The following 132 pages are in this category, out of 132 total. ... Karger's algorithm; KHOPCA clustering algorithm; Kleitman ...
The Karger–Stein variant of Karger's algorithm provides a faster randomized algorithm for determining the connectivity, with expected runtime (). [ 5 ] A related problem: finding the minimum k -edge-connected spanning subgraph of G (that is: select as few as possible edges in G that your selection is k -edge-connected) is NP-hard for k ≥ ...
The key insight to the algorithm is a random sampling step which partitions a graph into two subgraphs by randomly selecting edges to include in each subgraph. The algorithm recursively finds the minimum spanning forest of the first subproblem and uses the solution in conjunction with a linear time verification algorithm to discard edges in the graph that cannot be in the minimum spanning tree.
A simple greedy algorithm that achieves this approximation factor computes a minimum cut in each of the connected components and removes the lightest one. This algorithm requires a total of n − 1 max flow computations. Another algorithm achieving the same guarantee uses the Gomory–Hu tree representation of minimum cuts.
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.