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Contraction (cont)

Analysis:

V … number of vertices

  • Probability of contract to result in a minimum cut:
    ≥ `1 // ``((V),(2))`
  • This is much higher than the probability of picking a minimum cut at random, which is
    `((V),(2))` `// (2^(V-1) - 1)`
    because every graph has 2V-1-1 cuts, of which at most `((V),(2))` can have minimum weight
  • Single edge contraction can be implemented in O(V) time on an adjacency-list representation ⇒ total running time: O(V2)

    (Best known implementation uses O(E) time)