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Parameterized Algorithms
TLDR
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. Expand
On Multiway Cut Parameterized above Lower Bounds
In this paper we consider two above lower bound parameterizations of the NodeMultiway Cut problem -- above the maximum separating cut and above a natural LP-relaxation -- and prove them to beExpand
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
TLDR
It is shown that the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like Cycle Packing, and in several cases it is able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail. Expand
Designing FPT Algorithms for Cut Problems Using Randomized Contractions
We introduce a new technique for designing fixed-parameter algorithms for cut problems, namely randomized contractions. With our framework: (1) We obtain the first FPT algorithm for the parameterizedExpand
Polynomial bounds for centered colorings on proper minor-closed graph classes
TLDR
The first polynomial upper bounds on the number of colors needed in p-centered colorings of graphs drawn from proper minor-closed classes are provided, which answers an open problem posed by Dvoř{a}k. Expand
A ck n 5-Approximation Algorithm for Treewidth
TLDR
This is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in $k$ and linear in the input size and can be used to speed up many algorithms to work in time. Expand
Optimal Parameterized Algorithms for Planar Facility Location Problems Using Voronoi Diagrams
TLDR
A general family of facility location problems defined on planar graphs and on the 2-dimensional plane is studied, showing that the time brute force algorithm of selecting k objects can be improved to \(n^{{\mathcal{O}}(\sqrt{k})}\) time. Expand
Parameterized Complexity of Eulerian Deletion Problems
TLDR
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. Expand
Fixed-Parameter Tractable Canonization and Isomorphism Test for Graphs of Bounded Treewidth
TLDR
A fixed-parameter tractable algorithm that, given a parameter k and two graphs G, either concludes that one of these graphs has treewidth at least k, or determines whether G and G are isomorphic, which in fact solves the more general canonization problem. Expand
Clique Cover and Graph Separation: New Incompressibility Results
TLDR
This article shows that, unless the polynomial hierarchy collapses to its third level, the following parameterized problems do not admit aPolynomial-time preprocessing algorithm that reduces the size of an instance to polynometric in the parameter. Expand
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