Karger’s Algorithm Assignment Help

Karger's algorithm is really a randomized algorithm in order to compute a minimum cut of a connected graph. It had been created through David Karger and first published in 1993.

Clustering via graph cuts

The minimum cut of an undirected graph G = (V, E) is a partition of the nodes into two groups V1 and V2 (that is, V = V1 ∪ V2 and, V1 ∩ V2 = ∅), so that the number of edges between V1 and V2 is minimized. In the graph, for instance, the minimum cut has size two and partitions the nodes into.

Here’s the randomized algorithm with regard to finding the minimum cut:

• Repeat until just two nodes remain
  • Pick an edge of G at random and collapse its two endpoints into a single node
• For the two remaining nodes u1 as well as u2 set V1 = nodes that went into u1 and V2 = nodes in u2