1) The document discusses dominator trees and feedback cuts for a graph. 2) It provides the pre-order and post-order traversals for the dominator tree and post dominator tree of the graph. 3) The document also presents the total time complexity of O(N+E*D) for an algorithm to compute dominator sets, where N is the graph size, E is the number of edges, and D is the size of the largest dominator set.

1. D(5) = entry; D(1) = exit; D(4) = P(4)UD(4) = D(5)UD(4) = {5,4}; D(3) = P(3)UD(3) = D(5)UD(3) = {5,3}; D(2) = P(2)UD(2) = D(3)UD(2) = {5,3,2}; @ Pre(3) D(1) = P(1)UD(1) = D(5)UD(1) = {5,1}; D(2) = P(2)UD(3) = D(1)UD(2) = {5,,3,2}&{5,1}UD(2) @ Pre(1) = {5,2}

2. Post dominator tree pre order {3,4,5,2,1} post_order {1,4,5,2,3} Dominator tree pre order {5,1,2,3,4} post order {1,2,3,4,5} Feedback cut @ 1 5 1 3 2 4 5 1 3 3 2 4 2

3. A Simple, Fast Dominance Algorithm

4. 1 2 3 6 5 1 2 3 4 6 5 1 2 3 4 6 5 1 2 3 4

5. Thus, the total cost per iteration is O(N + E · D) D is the size ofthe largest Dom set.

6. E is taken over the entire traversal

7. N is traversing the graph to compute the reverse postorder sequence