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In computational geometry, a standard technique to build a structure like a convex hull or Delaunay triangulation is to randomly permute the input points and then insert them one by one into the existing structure. The randomization ensures that the expected number of changes to the structure caused by an insertion is small, and so the expected running time of the algorithm can be bounded from above. This technique is known as randomized incremental construction.cite-ref-19[19]

Input: A graph G(V,E)

Output: A cut partitioning the vertices into L and R, with the minimum number of edges between L and R.

Recall that the contraction of two nodes, u and v, in a (multi-)graph yields a new node u ' with edges that are the union of the edges incident on either u or v, except from any edge(s) connecting u and v. Figure 1 gives an example of contraction of vertex A and B. After contraction, the resulting graph may have parallel edges, but contains no self loops.

Karger'scite-ref-20[20] basic algorithm:

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