Problem 5. The max-bottleneck path problem:

1. Create a directed graph for the given undirected graph:

add directed edges(u->v, v->u) between every pair of vertices u & v

2. Initialize s as starting vertex

3. while there is a path from s to v:

for each edge {u,v} :

remove u->v

check v->u is there :

if no : add v->u

4. Label each label whether or not reachable from s

5. Create a set B of edges which is the set of bottleneck edges:

if edge connects a reachable and a non reachable vertex

Prove the correctness of algorithm and analyze its running time.