An approximation algorithm for the-pseudoforest deletion problem

Mugang Lin, Qilong Feng, Bin Fu, Jianxin Wang

Abstract: Highlights•This paper studies a generalization of the FVS problem, called the l-pseudoforest deletion problem. The FVS problem is its special case with l=0<math><mi is="true">l</mi><mo linebreak="goodbreak" linebreakstyle="after" is="true">=</mo><mn is="true">0</mn></math>.•By extracting a sequence of subgraphs with some structure and special weight, and splitting a graph into decomposition subgraphs. This paper presents a polynomial time approximation algorithm for the l-Pseudoforest Deletion problem.•We obtain the approximation ratio 4l of the algorithm when l>0<math><mi is="true">l</mi><mo linebreak="goodbreak" linebreakstyle="after" is="true">&gt;</mo><mn is="true">0</mn></math> by analyzing the properties and local ratio of the decomposition subgraphs.•By further analyzing local ratio of the decomposition subgraphs, we obtain an interesting approximation ratio 2 for the problem with l=1<math><mi is="true">l</mi><mo linebreak="goodbreak" linebreakstyle="after" is="true">=</mo><mn is="true">1</mn></math>, which matches the current best constant approximation factor for the FVS problem.