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Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…

Computational Complexity · Computer Science 2017-08-28 Henning Fernau , Till Fluschnik , Danny Hermelin , Andreas Krebs , Hendrik Molter , Rolf Niedermeier

The Vertex Cover problem plays an essential role in the study of polynomial kernelization in parameterized complexity, i.e., the study of provable and efficient preprocessing for NP-hard problems. Motivated by the great variety of positive…

Computational Complexity · Computer Science 2019-05-10 Eva-Maria C. Hols , Stefan Kratsch , Astrid Pieterse

The Maximum Betweenness Centrality problem (MBC) can be defined as follows. Given a graph find a $k$-element node set $C$ that maximizes the probability of detecting communication between a pair of nodes $s$ and $t$ chosen uniformly at…

Data Structures and Algorithms · Computer Science 2010-08-23 Martin Fink , Joachim Spoerhase

Kernelization is an important tool in parameterized algorithmics. Given an input instance accompanied by a parameter, the goal is to compute in polynomial time an equivalent instance of the same problem such that the size of the reduced…

Computational Complexity · Computer Science 2018-10-23 Till Fluschnik , George B. Mertzios , André Nichterlein

We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total…

Data Structures and Algorithms · Computer Science 2022-07-04 Benjamin Merlin Bumpus , Bart M. P. Jansen , Jari J. H. de Kroon

Enumerative kernelization is a recent and promising area sitting at the intersection of parameterized complexity and enumeration algorithms. Its study began with the paper of Creignou et al. [Theory Comput. Syst., 2017], and development in…

Data Structures and Algorithms · Computer Science 2025-09-11 Marin Bougeret , Guilherme C. M. Gomes , Vinicius F. dos Santos , Ignasi Sau

An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a…

Data Structures and Algorithms · Computer Science 2021-01-12 Petr A. Golovach , Christian Komusiewicz , Dieter Kratsch , Van Bang Le

An important result in the study of polynomial-time preprocessing shows that there is an algorithm which given an instance (G,k) of Vertex Cover outputs an equivalent instance (G',k') in polynomial time with the guarantee that G' has at…

Data Structures and Algorithms · Computer Science 2015-03-17 Bart M. P. Jansen , Hans L. Bodlaender

In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph $G$ and a positive integer $k$, and the objective is to decide whether $G$ contains a minimal vertex cover of size at least $k$. Motivated by the kernelization of MMVC…

Data Structures and Algorithms · Computer Science 2021-12-20 Júlio Araújo , Marin Bougeret , Victor A. Campos , Ignasi Sau

We consider the problem of inference for parameters selected to report only after some algorithm, the canonical example being inference for model parameters after a model selection procedure. The conditional correction for selection…

Methodology · Statistics 2019-01-30 Jelena Markovic , Jonathan Taylor , Jeremy Taylor

For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and for every…

Data Structures and Algorithms · Computer Science 2011-10-17 Eun Jung Kim , Ryan Williams

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…

Optimization and Control · Mathematics 2015-03-19 Mickaël Binois , David Ginsbourger , Olivier Roustant

Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is…

Machine Learning · Statistics 2018-11-09 Kelvin Hsu , Richard Nock , Fabio Ramos

Betweenness centrality---measuring how many shortest paths pass through a vertex---is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [J. Math.…

Data Structures and Algorithms · Computer Science 2020-05-14 Matthias Bentert , Alexander Dittmann , Leon Kellerhals , André Nichterlein , Rolf Niedermeier

We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound…

Cryptography and Security · Computer Science 2021-05-17 Jonathan Ullman

The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…

Computational Complexity · Computer Science 2013-12-23 Henry Yuen

In parameterized complexity, it is well-known that a parameterized problem is fixed-parameter tractable if and only if it has a kernel - an instance equivalent to the input instance, whose size is just a function of the parameter. The size…

Data Structures and Algorithms · Computer Science 2023-03-07 Ashwin Jacob , Diptapriyo Majumdar , Venkatesh Raman

An $\alpha$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(\alpha c)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute…

Data Structures and Algorithms · Computer Science 2023-07-06 Stefan Kratsch , Pascal Kunz

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…

Statistics Theory · Mathematics 2013-05-06 Victor Chernozhukov , Sokbae Lee , Adam M. Rosen

We consider a class of bi-parameter kernels and related square functions in the upper half-space, and give an efficient proof of a boundedness criterion for them. The proof uses modern probabilistic averaging methods and is based on…

Classical Analysis and ODEs · Mathematics 2014-11-11 Henri Martikainen