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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...
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.
