An improved kernel for the undirected planar feedback vertex set problem

Authors:
Faisal N. Abu-Khzam;Mazen Bou Khuzam
Affiliations:
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon;Department of Mathematics, Kuwait University, Al Safat, Kuwait
Venue:
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Year:
2012

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Abstract

We consider the parameterized Feedback Vertex Set problem on unweighted, undirected planar graphs. We present a kernelization algorithm that takes a planar graph G and an integer k as input and either decides that (G,k) is a no instance or produces an equivalent (kernel) instance (G′,k′) such that k′≤k and |V(G′)|k. In addition to the improved kernel bound (from 112k to 97k), our algorithm features simple linear-time reduction procedures that can be applied to the general Feedback Vertex Set problem.