• Publications
  • Influence
Kernelization Lower Bounds by Cross-Composition
TLDR
We introduce the framework of cross-composition for proving kernelization lower bounds for a number of important graphs problems with structural (nonsta... Expand
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Deterministic Single Exponential Time Algorithms for Connectivity Problems Parameterized by Treewidth
TLDR
We present two new approaches rooted in linear algebra, based on matrix rank and determinants, which provide deterministic c tw | V | O ( 1 ) time algorithms, also for weighted and counting versions of connectivity problems; we show how to evaluate those formulas via dynamic programming. Expand
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Representative Sets and Irrelevant Vertices: New Tools for Kernelization
TLDR
We show how representative sets can be used to give a polynomial kernel for the elusive Almost 2-sat problem (where the task is to remove at most k clauses to make a 2-CNF formula satisfiable), solving a major open problem in kernelization. Expand
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Cross-Composition: A New Technique for Kernelization Lower Bounds
TLDR
We introduce a new technique for proving kernelization lower bounds, called cross-composition. Expand
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Compression via Matroids: A Randomized Polynomial Kernel for Odd Cycle Transversal
TLDR
The Odd Cycle Transversal problem (OCT) asks whether a given undirected graph can be made bipartite by deleting at most k of its vertices. Expand
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A Completeness Theory for Polynomial (Turing) Kernelization
TLDR
The framework of Bodlaender et al. (J Comput Sys Sci 75(8):423–434, 2009) and Fortnow and Santhanam allows us to exclude the existence of Turing kernels for a range of problems under reasonable complexity-theoretical assumptions. Expand
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Recent developments in kernelization: A survey
  • S. Kratsch
  • Computer Science, Mathematics
  • Bull. EATCS
  • 19 June 2014
TLDR
Kernelization is a formalization of efficient preprocessing, aimed mainly at combinatorially hard problems. Expand
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Two Edge Modification Problems without Polynomial Kernels
Given a graph G and an integer k, the ? Edge Completion/Editing/Deletion problem asks whether it is possible to add, edit, or delete at most k edges in G such that one obtains a graph that fulfillsExpand
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Bin packing with fixed number of bins revisited
TLDR
We show, by proving the W[1]-hardness of Unary Bin Packing (where the sizes are given in unary encoding), that the problem can be solved in time n^O^(^k^) for an input of length n by dynamic programming. Expand
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Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem
TLDR
We show that evolutionary algorithms solve the vertex cover problem efficiently if the size of a minimum vertex cover is not too large, i.e., the expected runtime is bounded by a function in the parameter. Expand
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