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Efficient Recruiting Research Paper

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Efficient Recruiting is NP: Given a set of k counselors, it can be checked in polynomial time that at least one counselor is qualified in each of the n sports. Vertex Cover is known to be NP-complete (8.16). Vertex Cover ≤P Efficient Recruiting: Suppose we have a black box for Efficient Recruiting and want to solve an instance of Vertex Cover. For our Vertex Cover Problem, we have a graph G=(V,E) and a number k, and need to find out if G contains a vertex cover of size (at most) k. We need to reduce the Vertex Cover Problem to an Efficient Recruiting Problem. We do this by assigning each counselor to a node and each edge represents some sport. Each counselor is qualified in the sports for which the sports edge is incident on their corresponding
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