FPT algorithms for Connected Feedback Vertex Set

  • Authors:

  • Neeldhara Misra;Geevarghese Philip;Venkatesh Raman;Saket Saurabh;Somnath Sikdar

  • Affiliations:

  • The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;The Institute of Mathematical Sciences, Chennai, India;RWTH Aachen University, Aachen, Germany

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2012

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Abstract

We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a graph G=(V,E) and an integer k, decide whether there exists F驴V, |F|驴k, such that G[V驴F] is a forest and G[F] is connected.We show that Connected Feedback Vertex Set can be solved in time O(2 O(k) n O(1)) on general graphs and in time $O(2^{O(\sqrt{k}\log k)}n^{O(1)})$ on graphs excluding a fixed graph H as a minor. Our result on general undirected graphs uses, as a subroutine, a parameterized algorithm for Group Steiner Tree, a well studied variant of Steiner Tree. We find the algorithm for Group Steiner Tree of independent interest and believe that it could be useful for obtaining parameterized algorithms for other connectivity problems.