15-451 MINI #4: due midnight Oct 30, 2007.
1. (a) What is the maximum s-t flow in the graph G below?
(b) Draw the residual graph you get at the very end of running the
Ford-Fulkerson algorithm on this graph. (There is more than
one legal answer)
3 5
s------->a-------->b
| ^ |
|4 |3 |4
| | |
v 5 | 2 v
c------->d-------->t
2. Suppose we use the Ford-Fulkerson algorithm to solve a Maximum
Bipartite Matching problem. The very first path P found will
necessarily have only 3 edges in it, but it is possible for later
iterations to find paths of more than 3 edges. E.g., in the
example in class on Tuesday, the last path found had 5 edges. Give
an example of a bipartite graph where it is possible for one of the
paths found to use 9 edges.