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- W2891457632 abstract "The Chordal Vertex Deletion (ChVD) problem asks to delete a minimum number of vertices from an input graph to obtain a chordal graph. In this paper we develop a polynomial kernel for ChVD under the parameterization by the solution size. Using a new Erdös--Pósa-type packing/covering duality for holes in nearly chordal graphs, we present a polynomial-time algorithm that reduces any instance $(G,k)$ of ChVD to an equivalent instance with ${poly}(k)$ vertices. The existence of a polynomial kernel answers an open problem posed by Marx in 2006 [D. Marx, “Chordal Deletion Is Fixed-Parameter Tractable,” in Graph-Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 4271, Springer, 2006, pp. 37--48]. To obtain the kernelization, we develop the first ${poly}({sc opt})$-approximation algorithm for ChVD, which is of independent interest. In polynomial time, it either decides that $G$ has no chordal deletion set of size $k$, or outputs a solution of size $mathcal{O}(k^4log^2k)$." @default.
- W2891457632 created "2018-09-27" @default.
- W2891457632 creator A5048942396 @default.
- W2891457632 creator A5059330513 @default.
- W2891457632 date "2018-01-01" @default.
- W2891457632 modified "2023-09-27" @default.
- W2891457632 title "Approximation and Kernelization for Chordal Vertex Deletion" @default.
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- W2891457632 doi "https://doi.org/10.1137/17m112035x" @default.
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