[prev] 37 [next]

Karger's Algorithm (cont)

Analysis:

V … number of vertices
E … number of edges

  • Probability of success: `>= 1 - 1/V`
    • probability of not finding a minimum cut when the contraction algorithm is repeated `d = ` `((V),(2))``* ln V`  times:
      `<= [1 - 1 // ((V),(2))]^d <= 1 / e^(ln V) = 1 / V`
  • Total running time: O(E·d) = O(E·V2·log V)
    • assuming edge contraction implemented in O(E)