Approximating Partially Bounded Degree Deletion on Directed Graphs

The Bounded Degree Deletion problem (BDD) is that of computing a minimum vertex set in a graph \(G=(V, E)\) with degree bound \(b: V\rightarrow \mathbb {Z}_+\), such that, when it is removed from G, the degree of any remaining vertex v is no larger than b(v). It is a classic problem in graph theory and various results have been obtained including an approximation ratio of \(2+\ln b_{\max }\) [30], where \(b_{\max }\) is the maximum degree bound.