Book Chapter10.1007/978-3-540-77120-3_79
Problem kernels for NP-complete edge deletion problems: split and related graphs
Jiong Guo
- 17 Dec 2007
- pp 915-926
TL;DR: This work presents the seemingly first non-trivial algorithmic results for these four NP-complete edge deletion problems, namely, four polynomial-time data reduction algorithms that achieve problem kernels containing O(k2), O (k4), O(K3), and O( k3) vertices, respectively.
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Abstract: In an edge deletion problem one is asked to delete at most k edges from a given graph such that the resulting graph satisfies a certain property. In this work, we study four NP-complete edge deletion problems where the goal graph has to be a chain, a split, a threshold, or a co-trivially perfect graph, respectively. All these four graph classes are characterized by a common forbidden induced subgraph 2K2, that is, an independent pair of edges. We present the seemingly first non-trivial algorithmic results for these four problems, namely, four polynomial-time data reduction algorithms that achieve problem kernels containing O(k2), O(k4), O(k3), and O(k3) vertices, respectively.
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Citations
•Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
- 27 Jul 2015
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
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Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
169
Two edge modification problems without polynomial kernels
Stefan Kratsch,Magnus Wahlström +1 more
TL;DR: This paper answers an open problem posed by Cai, namely, whether the Π Edge Deletion problem, parameterized by the number of deletions, admits a polynomial kernelization when Π can be characterized by a finite set of forbidden induced subgraphs.
86
Two Edge Modification Problems without Polynomial Kernels
Stefan Kratsch,Magnus Wahlström +1 more
- 02 Dec 2009
TL;DR: A graph H on seven vertices is presented such that $\mathcal{H}$-free Edge Deletion and H- free Edge Editing do not admit polynomial kernelizations, unless $\mbox{NP}\subseteq \mbox {coNP}/\mbox ${poly}$.
75
Parameterized Complexity of Eulerian Deletion Problems.
TL;DR: A randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges, based on a novel application of the color coding technique is shown, proving that this is not possible unless NP⊆coNP/poly.
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