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Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
TLDR
We show that no NP-hard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of O(k2-ε) edges unless coNP is in NP/poly, which implies that the polynomial-time hierarchy collapses to its third level. Expand
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On Problems as Hard as CNF-SAT
TLDR
The field of exact exponential time algorithms for NP-hard problems has thrived over the last decade. Expand
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Kernelization of packing problems
TLDR
Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. Expand
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Homomorphisms are a good basis for counting small subgraphs
TLDR
We introduce graph motif parameters, a class of graph parameters that depend only on the frequencies of constant-size induced subgraphs. Expand
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Exponential Time Complexity of the Permanent and the Tutte Polynomial
TLDR
We show conditional lower bounds for well-studied #P-hard problems: The number of satisfying assignments of a 2-CNF formula with <i>n</i> variables cannot be computed in time exp(<i>o</i>(<i>) and the same is true for computing the number of all independent sets in a graph. Expand
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The PACE 2017 Parameterized Algorithms and Computational Experiments Challenge: The Second Iteration
TLDR
In this article, the Program Committee of the Second Parameterized Algorithms and Computational Experiments challenge (PACE 2017) reports on the second iteration of the PACE challenge. Expand
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The First Parameterized Algorithms and Computational Experiments Challenge
TLDR
In this article, the steering committee of the Parameterized Algorithms and Computational Experiments challenge reports on the first iteration of the challenge. Expand
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Fine-grained reductions from approximate counting to decision
TLDR
In this paper, we introduce a general framework for fine-grained reductions of approximate counting problems to their decision versions. Expand
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Complexity of the Cover Polynomial
TLDR
In this paper, we show that, in almost the whole plane, the problem of evaluating the cover polynomial is #Phard to evaluate at all but a few special points and curves. Expand
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Lovász Meets Weisfeiler and Leman
TLDR
In this paper, we relate a beautiful theory by Lov\'asz with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k-dimensional generalization known as the Weisfeiler-Leman algorithm. Expand
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