1. What is the definition of a safe edge for the minimum spanning tree algorithm? 2....

Question

Question

1. What is the definition of a safe edge for the minimum spanning tree algorithm?

2. Give an example graph with 4 nodes and 5 edges with exactly three strongly connected components.

3. What is the running time of the Kruskal spanning tree algorithm on a graph with n nodes and n log n edges?

engineering Computer-Science

Answer 1

Answer #1

1)

A safe edge is am edge that may be added to a tree T without violating the invariant that T is a subset of some minimum spanning tree.

2)

3)

Kruskal Algorithm runs in O(E log V) time.

In this case, E = log n and V = n

Hence, total running time = O(log²n)

Answer 2

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