Bob is throwing a party to celebrate a new road network that connects n cities. He...

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Bob is throwing a party to celebrate a new road network that connects n cities. He decides to invite n-1 guests, one from each city other than his own city. Each invited guest plans to drive to the party using the road network, which can be modeled as a directed graph G = (V, E) between cities. In this road network, if there is a road from one city to another, then there is no road in the opposite direction.³ Bob just realized he has invited one person too many. He does not want to be rude and uninvite anyone, but he wants to make sure that at least one person will be unable to reach his house. Therefore, naturally, he enlists the help of his friend Sabo Taj¹ to block some of the roads. More precisely, here is Sabo's task: Sabo needs to identify a set FCE of roads of minimum cardinality such that if these roads are blocked, at least one guest cannot attend the party. Describe how Sabo can identify such a set F of minimum cardinality by reducing the problem to a maximum flow problem. The algorithm you describe should be simple (most of the work is done by solving one or more maximum flow problems) and efficient (it should run in polynomial time). Be sure to briefly explain why your algorithm correctly solves Sabo's task. Bob is throwing a party to celebrate a new road network that connects n cities. He decides to invite n-1 guests, one from each city other than his own city. Each invited guest plans to drive to the party using the road network, which can be modeled as a directed graph G = (V, E) between cities. In this road network, if there is a road from one city to another, then there is no road in the opposite direction.³ Bob just realized he has invited one person too many. He does not want to be rude and uninvite anyone, but he wants to make sure that at least one person will be unable to reach his house. Therefore, naturally, he enlists the help of his friend Sabo Taj¹ to block some of the roads. More precisely, here is Sabo's task: Sabo needs to identify a set FCE of roads of minimum cardinality such that if these roads are blocked, at least one guest cannot attend the party. Describe how Sabo can identify such a set F of minimum cardinality by reducing the problem to a maximum flow problem. The algorithm you describe should be simple (most of the work is done by solving one or more maximum flow problems) and efficient (it should run in polynomial time). Be sure to briefly explain why your algorithm correctly solves Sabo's task.

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Sabo can identify a set of minimum cardinality roads to block by reducing the problem to a maximum flow problem and then applying a standard algorithm ... View the full answer