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FPT algorithms for Connected Feedback Vertex Set

Author

Listed:
  • Neeldhara Misra

    (The Institute of Mathematical Sciences)

  • Geevarghese Philip

    (The Institute of Mathematical Sciences)

  • Venkatesh Raman

    (The Institute of Mathematical Sciences)

  • Saket Saurabh

    (The Institute of Mathematical Sciences)

  • Somnath Sikdar

    (RWTH Aachen University)

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⊆V, |F|≤k, such that G[V∖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.

Suggested Citation

  • Neeldhara Misra & Geevarghese Philip & Venkatesh Raman & Saket Saurabh & Somnath Sikdar, 2012. "FPT algorithms for Connected Feedback Vertex Set," Journal of Combinatorial Optimization, Springer, vol. 24(2), pages 131-146, August.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:2:d:10.1007_s10878-011-9394-2
    DOI: 10.1007/s10878-011-9394-2
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