Suppose that G = (V, E) is a directed graph with |V| = n and JE| = m unless otherwise stated. Also suppose that all edge capacities are integral and that there are no directed 2-cycles. Then consider the following network with edge capacities. Assume that M E Z2 .

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Suppose that G = (V, E) is a directed graph with |V| = n and |E| = m unless
otherwise stated. Also suppose that all edge capacities are integral and that there are no
directed 2-cycles.
Then consider the following network with edge capacities.
Assume that M E Z,2 .
M.
(3
M
M
M
| 1
M
M
5 M
M
(a) Explain how the Ford-Fulkerson algorithm could take M or more iterations on this
graph.
(b) Run the Edmonds-Karp algorithm on this network. Be sure to give the flow after each
iteration
Transcribed Image Text:Suppose that G = (V, E) is a directed graph with |V| = n and |E| = m unless otherwise stated. Also suppose that all edge capacities are integral and that there are no directed 2-cycles. Then consider the following network with edge capacities. Assume that M E Z,2 . M. (3 M M M | 1 M M 5 M M (a) Explain how the Ford-Fulkerson algorithm could take M or more iterations on this graph. (b) Run the Edmonds-Karp algorithm on this network. Be sure to give the flow after each iteration
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