When asked to give an algorithm that meets a certain time bound, you need to give the algorithm (pseudocode/description) and analyze its running time to show that it meets the required bound.
1. Consider the following two variations of the maximum ﬂow problem.
(a) Given a ﬂow network with multiple sources and multiple sinks, compute a maximum ﬂow from the sources to the sinks (i.e., a ﬂow that maximizes the total amount of ﬂow out of all the sources. Note that the ﬂow must satisfy all the three constraints).
(b) Given a ﬂow network in which the nodes as well as the edges have capacities (positive integers), compute a maximum ﬂow from s to t that respects the node capacities as well (i.e., for every node in the network, the total amount of ﬂow out of the node should be bounded above by the capacity of the node).
Show, by reductions to the maximum ﬂow problem, that the above two problems can be solved in time O(n3), where n is the number of nodes in the network.
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