Question: Problem 1 [DPV] Problem 7.18 (a) (b) Solve the following problems by reducing to the original max-flow problem. In other words, explain how to solve

Problem 1 [DPV] Problem 7.18 (a) (b)

Solve the following problems by reducing to the original max-flow problem. In other words, explain how to solve the new flow variant problem using an algorithm for solving max-flow as a black-box. Explain how to take an input for the new problem and define an input for the original max-flow problem. Then given a max-flow f to this input you just defined, explain how to get the solution to the new problem.

You should describe your algorithm in words (a list is okay); no pseudocode. (a) There are many sources and many sinks, and we wish to maximize the total flow

from all sources to all sinks.

(b) Each vertex also has a capacity on the maximum flow that can enter it.

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