Hitting forbidden minors: Approximation and Kernelization

28th International Symposium on Theoretical Aspects of Computer Science

Fedor V. Fomin1 ; Daniel Lokshtanov2 ; Neeldhara Misra3 ; Geevarghese Philip3 ; Saket Saurabh3 ; 2 University of California ; San Diego ; Department of Computer Science and Engineering ; 9500 Gilman Drive ; La Jolla ; CA 92093-0404 ; USA ; 3 The Institute of Mathematical Sciences ; Chennai 600113 ; India.

Others  :  http://drops.dagstuhl.de/opus/volltexte/2011/3010/pdf/20.pdf
PID  :  44749

来源: CEUR

【 摘 要 】

We study a general class of problems called p-F-Deletion problems. In an p-F-Deletion problem, we are asked whether a subset of at most k vertices can be deleted from a graph G such that the resulting graph does not contain as a minor any graph from the family F of forbidden minors. We obtain a number of algorithmic results on the p-F-Deletion problem when F contains a planar graph. We givea linear vertex kernel on graphs excluding t-claw K 1,t, the star with t leves, as an induced subgraph, where t is a fixed integer.an approximation algorithm achieving an approximation ratio of O(log 3/2OPT ), where OPT is the size of an optimal solution on general undirected graphs.Finally, we obtain polynomial kernels for the case when F only contains graph θ c as a minor for a fixed integer c. The graph θ c consists of two vertices connected by c parallel edges. Even though this may appear to be a very restricted class of problems it already encompasses well-studied problems such as Vertex Cover, Feedback Vertex Set and Diamond Hitting Set. The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes.