This problem deals with the Karger-Klein-Tarjan MST algorithm (KKT): Suppose that we modify KKT so that...
This problem deals with the Karger-Klein-Tarjan MST algorithm (KKT):
Suppose that we modify KKT so that instead of running two Boruvka ˙ steps, we only run one. Can we still claim that the expected running time of the algorithm is O(m)? Explain your answer.
Homework Answers
so on that each pass takes time via a single pass through the edges and followed by a pass over the edges to be colored blue
One can easily prove by induction that, after pass k of Boruvka's algorithm, each blue tree contains at least 2^k vertices , which implies that Boruvka's algorithm stops after at most lgn passes and runs intime at o(m)time per pass
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