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Meta-kernelization theorems are general results that provide polynomial kernels for large classes of parameterized problems. The known meta-kernelization theorems, in particular the results of Bodlaender et al. (FOCS'09) and of Fomin et al.…

Data Structures and Algorithms · Computer Science 2013-04-22 Robert Ganian , Friedrich Slivovsky , Stefan Szeider

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

Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been…

Data Structures and Algorithms · Computer Science 2015-07-21 Eduard Eiben , Robert Ganian , Stefan Szeider

The composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability…

Computational Complexity · Computer Science 2017-12-27 Till Fluschnik , Danny Hermelin , André Nichterlein , Rolf Niedermeier

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

In this paper, we devise a scheme for kernelizing, in sublinear space and polynomial time, various problems on planar graphs. The scheme exploits planarity to ensure that the resulting algorithms run in polynomial time and use O((sqrt(n) +…

Data Structures and Algorithms · Computer Science 2023-07-04 Arindam Biswas , Johannes Meintrup

Enumerative kernelization is a recent promising at the intersection of parameterized complexity and enumeration algorithms, with two proposed models. The first, known as enum-kernels and due to Creignou et al., was too permissive, leading…

Data Structures and Algorithms · Computer Science 2026-04-28 Marin Bougeret , Guilherme C. M. Gomes , Ignasi Sau

In this paper we consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization…

Data Structures and Algorithms · Computer Science 2013-06-25 Marek Cygan , Fabrizio Grandoni , Danny Hermelin

Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…

Data Structures and Algorithms · Computer Science 2010-10-04 Yixin Cao , Jianer Chen

We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same region as $B$. This problem is $\mathsf{NP}$-hard, but as for many $\mathsf{NP}$-hard problems…

Computational Geometry · Computer Science 2018-05-17 Jérémy Barbay , Pablo Pérez-Lantero , Javiel Rojas-Ledesma

Let F be a finite family of graphs. In the F-Deletion problem, one is given a graph G and an integer k, and the goal is to find k vertices whose deletion results in a graph with no minor from the family F. This may be regarded as a…

Data Structures and Algorithms · Computer Science 2026-01-21 Roohani Sharma , Michał Włodarczyk

We propose an efficient distributed online learning protocol for low-latency real-time services. It extends a previously presented protocol to kernelized online learners that represent their models by a support vector expansion. While such…

Machine Learning · Computer Science 2019-12-02 Michael Kamp , Sebastian Bothe , Mario Boley , Michael Mock

Kernel-phase is a data analysis method based on a generalization of the notion of closure-phase invented in the context of interferometry, but that applies to well corrected diffraction dominated images produced by an arbitrary aperture.…

Instrumentation and Methods for Astrophysics · Physics 2020-04-22 Frantz Martinache , Alban Ceau , Romain Laugier , Jens Kammerer , Mamadou N'Diaye , David Mary , Nick Cvetojevic , Coline Lopez

We study efficient preprocessing for the undirected Feedback Vertex Set problem, a fundamental problem in graph theory which asks for a minimum-sized vertex set whose removal yields an acyclic graph. More precisely, we aim to determine for…

Data Structures and Algorithms · Computer Science 2022-06-10 David Dekker , Bart M. P. Jansen

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

We study kernelization of classic hard graph problems when the input graphs fulfill triadic closure properties. More precisely, we consider the recently introduced parameters closure number $c$ and the weak closure number $\gamma$ [Fox et…

Data Structures and Algorithms · Computer Science 2021-03-09 Tomohiro Koana , Christian Komusiewicz , Frank Sommer

Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial…

Computational Complexity · Computer Science 2015-07-14 Michael Etscheid , Stefan Kratsch , Matthias Mnich , Heiko Röglin

This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…

Machine Learning · Computer Science 2015-09-16 Corinna Cortes , Prasoon Goyal , Vitaly Kuznetsov , Mehryar Mohri

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

Machine Learning · Statistics 2020-11-13 Debolina Paul , Saptarshi Chakraborty , Swagatam Das , Jason Xu

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