The undirected feedback vertex set problem has a poly(k) kernel

Authors:
Kevin Burrage;Vladimir Estivill-Castro;Michael Fellows;Michael Langston;Shev Mac;Frances Rosamond
Affiliations:
Department of Mathematics, University of Queensland, Brisbane, QLD;Griffith University, Brisbane, QLD, Australia;School of EE & CS, University of Newcastle, Callaghan, NSW, Australia;Department of Computer Science, University of Tennessee, Knoxville, TN;Department of Mathematics, University of Queensland, Brisbane, QLD;The Retreat for the Arts and Sciences, Newcastle, Australia
Venue:
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Year:
2006

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Abstract

Resolving a noted open problem, we show that the Undirected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class Poly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G,k) to a decision-equivalent simplified instance (G′,k′) where k′ ≤k, and the number of vertices of G′ is bounded by a polynomial function of k. Our main result shows an O(k11) kernelization bound.