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We introduce a new framework for the analysis of preprocessing routines for parameterized counting problems. Existing frameworks that encapsulate parameterized counting problems permit the usage of exponential (rather than polynomial) time…

Data Structures and Algorithms · Computer Science 2023-08-07 Daniel Lokshtanov , Pranabendu Misra , Saket Saurabh , Meirav Zehavi

We study the existence of polynomial kernels, for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. Our main result is that a polynomial kernel for $k$-Dominating Set on…

Data Structures and Algorithms · Computer Science 2021-09-15 Édouard Bonnet , Eun Jung Kim , Amadeus Reinald , Stéphan Thomassé , Rémi Watrigant

We are pleased to dedicate this survey on kernelization of the Vertex Cover problem, to Professor Juraj Hromkovi\v{c} on the occasion of his 60th birthday. The Vertex Cover problem is often referred to as the Drosophila of parameterized…

Data Structures and Algorithms · Computer Science 2019-05-15 Michael R. Fellows , Lars Jaffke , Aliz Izabella Király , Frances A. Rosamond , Mathias Weller

Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…

Computational Complexity · Computer Science 2019-07-31 Hans-Joachim Böckenhauer , Elisabet Burjons , Martin Raszyk , Peter Rossmanith

For a finite collection of connected graphs $\mathcal{F}$, the $\mathcal{F}$-MINOR-DELETION problem consists in, given a graph $G$ and an integer $\ell$, deciding whether $G$ contains a vertex set of size at most $\ell$ whose removal…

Data Structures and Algorithms · Computer Science 2025-12-16 Marin Bougeret , Eric Brandwein , Ignasi Sau

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

We introduce and study two natural generalizations of the Connected VertexCover (VC) problem: the $p$-Edge-Connected and $p$-Vertex-Connected VC problem (where $p \geq 2$ is a fixed integer). Like Connected VC, both new VC problems are FPT,…

Data Structures and Algorithms · Computer Science 2022-08-23 Carl Einarson , Gregory Gutin , Bart M. P. Jansen , Diptapriyo Majumdar , Magnus Wahlstrom

In the last years, kernelization with structural parameters has been an active area of research within the field of parameterized complexity. As a relevant example, Gajarsk{\`y} et al. [ESA 2013] proved that every graph problem satisfying a…

Data Structures and Algorithms · Computer Science 2018-06-07 Marin Bougeret , Ignasi Sau

We study provably effective and efficient data reduction for a class of NP-hard graph modification problems based on vertex degree properties. We show fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases…

Discrete Mathematics · Computer Science 2016-04-13 Vincent Froese , André Nichterlein , Rolf Niedermeier

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

A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…

Data Analysis, Statistics and Probability · Physics 2012-09-19 N. D. Gagunashvili , M. Schmelling

We investigate the relationship between several enumeration complexity classes and focus in particular on problems having enumeration algorithms with incremental and polynomial delay (IncP and DelayP respectively). We show that, for some…

Computational Complexity · Computer Science 2017-07-04 Florent Capelli , Yann Strozecki

In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As,…

Computational Complexity · Computer Science 2019-03-01 Jouke Witteveen , Ralph Bottesch , Leen Torenvliet

Given a graph $G$ and an integer $k$, the $H$-free Edge Deletion problem asks whether there exists a set of at most $k$ edges of $G$ whose deletion makes $G$ free of induced copies of $H$. Significant attention has been given to the…

Data Structures and Algorithms · Computer Science 2025-01-28 Séhane Bel Houari-Durand , Eduard Eiben , Magnus Wahlström

We study the CONNECTED \eta-TREEDEPTH DELETION problem where the input instance is an undireted graph G = (V, E) and an integer k. The objective is to decide if G has a set S \subseteq V(G) of at most k vertices such that G - S has…

Data Structures and Algorithms · Computer Science 2022-12-02 Eduard Eiben , Diptapriyo Majumdar , M. S. Ramanujan

Nowhere dense classes of graphs are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness,…

Discrete Mathematics · Computer Science 2018-09-06 Stephan Kreutzer , Roman Rabinovich , Sebastian Siebertz

Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…

Computational Complexity · Computer Science 2018-07-11 Max Bannach , Till Tantau

The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph that induces a connected subgraph. The problem is known to be fixed-parameter tractable (FPT), and is unlikely to have a polynomial sized kernel (under complexity…

Data Structures and Algorithms · Computer Science 2018-10-08 R. Krithika , Diptapriyo Majumdar , Venkatesh Raman

Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm…

Computer Vision and Pattern Recognition · Computer Science 2017-05-19 Jing Wang , Jie Shen , Ping Li

A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has…

Data Structures and Algorithms · Computer Science 2024-07-04 Guilherme C. M. Gomes , Emanuel Juliano , Gabriel Martins , Vinicius F. dos Santos