Introduction to algorithms study questions-bottleneck spanning tree

Row ideas, later pits.

A. Proof: The minimum spanning tree is the bottleneck spanning tree

A little evidence

B. Given figure G and integer B, determine whether the bottleneck spanning tree T value does not exceed B in linear time

Solution: DFS or BFS traverse graph G, skip the edge of the ownership value greater than B, and finally if the node does not traverse to, then the T value is greater than B, otherwise no more than B

C. Finding the bottleneck spanning tree T-value

1. Find out the median of the edge weight (similar to the problem of nth Element) M, in order to divide the edge of the graph G by weights into two parts, part less than or equal to M, and the other part greater than M

2. Using the method proposed by B to determine whether the T value of the bottleneck spanning tree is not more than M, that is to see if the T value is in the size of which half

3. If you are in a small half, delete the side of the large half and go back to step 1

4. If it is located on the half-edge, the small half of the graph must not be connected, the connecting components are shrunk to a point, and then the large half of a figure G2, and back to step 1

Note: The 4-step contraction process will be used to check the set

Introduction to algorithms study questions-bottleneck spanning tree