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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.
Known algorithms on graphs of bounded treewidth are probably optimal
TLDR
Lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth are obtained and the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi are proved.
Lower bounds based on the Exponential Time Hypothesis
TLDR
This chapter proves lower bounds based on ETH for the time needed to solve various problems, and in many cases these lower bounds match the running time of the best known algorithms for the problem.
(Meta) Kernelization
TLDR
The theorems unify and extend all previously known kernelization results for planar graph problems and show that all problems expressible in Counting Monadic Second Order Logic and satisfying a compactness property admit a polynomial kernel on graphs of bounded genus.
On Problems as Hard as CNF-SAT
TLDR
It is shown that, for every ϵ <; 1, the problems HITTING SET, SET SPLITTING, and NAE-SAT cannot be computed in time O(2ϵn) unless SETH fails, and it is proved that the fastest known algorithms for STEINTER TREE, CONNECTED VERTEX COVER, SET PARTITIONing, and the pseudo-polynomial time algorithm for SUBSET SUM cannot be significantly improved.
Slightly superexponential parameterized problems
TLDR
It is shown that the dependence on k in the running time of the best known algorithms cannot be improved to single exponential and three natural problems, arising from three different domains are proved to be solvable in time.
Incompressibility through Colors and IDs
TLDR
This paper shows how to combine results with combinatorial reductions which use colors and IDs in order to prove kernelization lower bounds for a variety of basic problems, and rules out the existence of compression algorithms for many of the problems in question.
Efficient Computation of Representative Sets with Applications in Parameterized and Exact Algorithms
TLDR
Two algorithms computing representative families of linear and uniform matroids are given and how to use representative families for designing single-exponential parameterized and exact exponential time algorithms are demonstrated.
Planar F-Deletion: Approximation, Kernelization and Optimal FPT Algorithms
TLDR
A number of generic algorithmic results about F-DELETION, when F contains at least one planar graph are obtained, which unify, generalize, and improve a multitude of results in the literature.
Graph Layout Problems Parameterized by Vertex Cover
TLDR
This paper study's basic ingredient is a classical algorithm for Integer Linear Programming when parameterized by dimension, designed by Lenstra and later improved by Kannan, showing that all the mentioned problems are fixed parameter tractable.
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