Problem 2 Reduce the following variations of the max flow problem to an input that can be solved running Ford- Fulkerson or Edmonds-Karp. You must explain in detail: how you build a (possibly) new network from the given scenario, that will serve as input to the algorithm, and how you recover the solution to the given problem from the output of your black box. (a) (Verter capacity) You are given a network G = {V,, Ce, 6, 8, t} where G, >0 is the capacity of each vertex and bounds the amount of flow that can enter the corresponding vertex. (b) Given a directed graph G = (V,), and vertices s,t eV, design an algorithm that outputs the maxi- mum number of verter-disjoint paths from s to t. Briefly justify its correctness and state and analyse its runtime. Hint: use part (a) with some particular capacities for the vertices