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Kernelization Lower Bounds by Cross-Composition
TLDR
If an NP-hard problem and/or-cross-composes into a parameterized problem $\mathcal{Q}$ does not admit a polynomial kernel unless $\mbox{NP}\subseteq \mbox {coNP/poly}$ and the polynometric hierarchy collapses, then the framework of cross-composition for proving kernelization lower bounds is introduced. Expand
Cross-Composition: A New Technique for Kernelization Lower Bounds
TLDR
It is shown that if an NP-hard problem cross-composes into a parameterized problem Q then Q does not admit a polynomial kernel unless thePolynomial hierarchy collapses, and its applicability is shown by proving kernelization lower bounds for a number of important graphs problems with structural (non-standard) parameterizations. Expand
Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter
TLDR
This work is one of the first examples of research in kernelization using a non-standard parameter, and shows that this approach can yield interesting computational insights. Expand
The First Parameterized Algorithms and Computational Experiments Challenge
TLDR
The steering committee of the Parameterized Algorithms and Computational Experiments challenge (PACE) reports on the first iteration of the challenge. Expand
Data reduction for graph coloring problems
TLDR
This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances, and shows that the existence of polynomial kernels for q-Coloring parameterized by the vertex-deletion distance to a graph class F is strongly related to a function f(q) which bounds the number of vertices which are needed to preserve the no-answer to an instance of q-List Coloring on F. Expand
Connect the dot: Computing feed-links for network extension
TLDR
It is shown that the optimal single connection (feed-link) can be computed in O(λ7(n )l ogn) time, where n is the number of vertices that bounds the face andλ7 (n) is the slightly superlinear maximum length of a Davenport- Schinzel sequence of order 7 on n symbols. Expand
Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity
TLDR
A new type of race in parameterized analysis is called for, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or polynomial kernels. Expand
Preprocessing for Treewidth: A Combinatorial Analysis through Kernelization
TLDR
This paper shows that Treewidth has a kernel with O(l3) vertices, where l denotes the size of a vertex cover, and a kernel of polynomial size, which implies that given an instance (G, k) ofTreewidth the authors can efficiently reduce its size to O((l*)4) Vertices. Expand
Approximation and Kernelization for Chordal Vertex Deletion
TLDR
A polynomial kernel for ChVD under the parameterization by the solution size, as well as poly(opt) approximation algorithm, which answers an open problem of Marx from 2006. Expand
Fine-Grained Parameterized Complexity Analysis of Graph Coloring Problems
TLDR
It is proved that if F F is the class of paths – some of the simplest graphs of unbounded treedepth – then no such algorithm can exist unless SETH SETH fails, and there is no universal constant θ θ such that q-Coloring parameterized by vertex cover can be solved in time. Expand
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