38
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 2
V
-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(V
2
)
(Best known implementation uses
O(E)
time)