A linear algorithm for minimum 1-identifying codes in oriented trees

Consider an oriented graph G=(V,A)G=(V,A), a subset of vertices C⊆VC⊆V, and an integer r⩾1r⩾1; for any vertex v∈Vv∈V, let Br-(v) denote the set of all vertices xx such that there exists a path from xx to vv with at most rr arcs. If for all vertices v∈Vv∈V, the sets Br-(v)∩C are all nonempty and different, then we call CC an rr-identifying code. We describe a linear algorithm which gives a minimum 11-identifying code in any oriented tree.