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CSE 521 : Design and Analysis of Algorithms I Spring 2016 Lecture 1 : Contraction Algorithm

In order to further understand the algorithm, we can think of its connection to clustering. Say you have K clusters such that most of the edges are inside the clusters. If we run Karger’s Algorithm, at the time we have K super-nodes, we can consider them as the clusters. Note that since there are a few edges between the clusters, the algorithm is more likely to contract intra cluster edges (as opposed to the inter-cluster edges. Theorem 1.1. For any min-cut (S, S̄), Karger’s algorithm returns (S, S̄) w.p at least 1 (n2) = 2 n(n−1) .