Question: Consider an undirected graphG (V,E) where each edge (i, j ) has a cost cij and each vertex i V a nonnegative penalty

Consider an undirected graphG (V,E) where each edge (i, j ) has a cost cij and each vertex i ∈ V a nonnegative penalty πi . In the Prize-Collecting Traveling Salesman Problem (PCTSP), the objective is to find a tour that visits a subset of the vertices such that the length of the tour plus the sum of penalties of all vertices not in the tour is as small as possible. Show that the problem can be formulated as a Longest Path Problem between two prespecified nodes of a new network.

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