The Maximum Carpool Matching problem is a star packing problem in directed graphs. Formally, given a directed graph G = (V,A), a capacity function c : V → N, and a weight function w : A → R+, a carpool matching is a subset of arcs, M ⊆ A, such that every v ∈ V satisfies: (i) din M (v) · dout M (v) = 0, (ii) din M (v) ≤ c(v), and (iii) dout M (v) ≤ 1. A vertex v for which dout M (v) = 1 is a pas...
