Constant Factor Approximation Algorithm for l-Pseudoforest Deletion Problem

Abstract

An l-pseudoforest is a graph each of whose connected component is at most l edges away from 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 \(G[V\setminus P]\) 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 \(l\ge 1\) by using the local ratio technique. When \(l=1\), we get a better approximation ratio 2 for the problem by further analyzing the algorithm, which matches the current best constant approximation factor for the Feedback Vertex Set problem.