Consider the following problem. You are managing a communication network, modeled by a directed graph G = (V, E). There are c users who are interested in making use of this network. User i (for each i = 1, 2, … c) issues a request to reserve a specific path Pi in G on which to transmit data.
You are interested in accepting as many of these path requests as possible, subject to the following restriction: if you accept both Pi and Pj, then Pi and Pj cannot share any nodes.
Thus, the Path Selection Problem asks: Given a directed graph G = (V, E), a set of requests P1,P2,... ,Pc–each of which must be a path in G–and a number k, is it possible to select at least k of the paths so that no two of the selected paths share any nodes?
Prove that Path Selection is NP-complete.
We need at least 10 more requests to produce the solution.
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The more requests, the faster the answer.