An approximation algorithm for the l-pseudoforest deletion problem

An l-pseudoforest is a graph each of whose connected components is at most l edges removal being a tree. The l-Pseudoforest Deletion problem is to delete a vertex set P of minimum weight from a given vertex-weighted graph G=(V,E) such that the remaining graph G[V∖P] is an l-pseudoforest. The Feedback Vertex Set problem is a special case of the l-Pseudoforest Deletion problem with l=0. In this paper, we present a polynomial time 4l-approximation algorithm for the l-Pseudoforest Deletion problem with l≥1 by using the local ratio technique. When l=1, we get a better approximation ratio 2 for the problem by further analyzing the local ratio, which matches the current best constant approximation factor for the Feedback Vertex Set problem.