COCOON 2011: Computing and Combinatorics pp 98-109

# On Parameterized Independent Feedback Vertex Set

• Neeldhara Misra
• Geevarghese Philip
• Venkatesh Raman
• Saket Saurabh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6842)

## Abstract

We investigate a generalization of the classical Feedback Vertex Set (FVS) problem from the point of view of parameterized algorithms. Independent Feedback Vertex Set (IFVS) is the “independent” variant of the FVS problem and is defined as follows: given a graph G and an integer k, decide whether there exists F ⊆ V(G), |F| ≤ k, such that G[V(G) ∖ F] is a forest and G[F] is an independent set; the parameter is k. Note that the similarly parameterized versions of the FVS problem — where there is no restriction on the graph G[F] — and its connected variant CFVS — where G[F] is required to be connected — have been extensively studied in the literature. The FVS problem easily reduces to the IFVS problem in a manner that preserves the solution size, and so any algorithmic result for IFVS directly carries over to FVSA. We show that IFVS can be solved in time O(5 k n O(1)) time where n is the number of vertices in the input graph G, and obtain a cubic (O(k 3)) kernel for the problem. Note the contrast with the CFVS problem, which does not admit a polynomial kernel unless CoNP ⊆ NP/Poly.

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## Authors and Affiliations

• Neeldhara Misra
• 1
• Geevarghese Philip
• 1
• Venkatesh Raman
• 1
• Saket Saurabh
• 1
1. 1.The Institute of Mathematical SciencesChennaiIndia