FPT Algorithms for Connected Feedback Vertex Set

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

doi:10.1007/978-3-642-11440-3_25

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Conference Paper

FPT Algorithms for Connected Feedback Vertex Set

MPS-Authors

There are no MPG-Authors in the publication available

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Misra, N., Philip, G., Raman, V., Saurabh, S., & Sikdar, S. (2010). FPT Algorithms for Connected Feedback Vertex Set. In M. S. Rahman, & S. Fujita (Eds.), WALCOM: Algorithms and Computation (pp. 269-280). Berlin: Springer. doi:10.1007/978-3-642-11440-3_25.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0019-DC05-8

Abstract

We study the recently introduced \textscConnected Feedback Vertex Set (CFVS)} problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical \textsc{Feedback Vertex Set} problem and is defined as follows: given a graph G=(V,E) and an integer k, decide whether there exists F\subseteq V, |F| ≤q k, such that G[V \setminus F] is a forest and G[F] is connected. We show that \textsc{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 \textsc{Group Steiner Tree}, a well studied variant of \textsc{Steiner Tree}. We find the algorithm for \textsc{Group Steiner Tree of independent interest and believe that it could be useful for obtaining parameterized algorithms for other connectivity problems.