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A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…

Computational Complexity · Computer Science 2026-05-05 Christian Komusiewicz , Nils Morawietz , Frank Sommer , Luca Pascal Staus

We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…

Machine Learning · Computer Science 2018-10-31 Marina Munkhoeva , Yermek Kapushev , Evgeny Burnaev , Ivan Oseledets

The problem of deciding the validity (QSAT) of quantified Boolean formulas (QBF) is a vivid research area in both theory and practice. In the field of parameterized algorithmics, the well-studied graph measure treewidth turned out to be a…

Computational Complexity · Computer Science 2020-07-06 Johannes Klaus Fichte , Markus Hecher , Andreas Pfandler

Let F be a finite set of graphs. In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F…

Data Structures and Algorithms · Computer Science 2020-11-03 Fedor Fomin , Daniel Lokshtanov , Neeldhara Misra , Saket Saurabh

Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time…

Data Structures and Algorithms · Computer Science 2024-02-21 Frank Kammer , Andrej Sajenko

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two…

Logic in Computer Science · Computer Science 2017-02-10 Johannes Fichte , Markus Hecher , Michael Morak , Stefan Woltran

For a family of graphs $\cal F$, the $\mathcal{F}$-Contraction problem takes as an input a graph $G$ and an integer $k$, and the goal is to decide if there exists $S \subseteq E(G)$ of size at most $k$ such that $G/S$ belongs to $\cal F$.…

Data Structures and Algorithms · Computer Science 2017-08-03 Akanksha Agrawal , Saket Saurabh , Prafullkumar Tale

In this paper, we introduce a new class of parameterized problems, which we call XALP: the class of all parameterized problems that can be solved in $f(k)n^{O(1)}$ time and $f(k)\log n$ space on a non-deterministic Turing Machine with…

Computational Complexity · Computer Science 2024-01-22 Hans L. Bodlaender , Carla Groenland , Hugo Jacob , Marcin Pilipczuk , Michał Pilipczuk

Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of…

Data Structures and Algorithms · Computer Science 2016-04-19 Amariah Becker

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…

Artificial Intelligence · Computer Science 2014-06-13 Serge Gaspers , Stefan Szeider

Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…

Data Structures and Algorithms · Computer Science 2019-02-21 Max Bannach , Malte Skambath , Till Tantau

For a graph $H$, a graph $G$ is an $H$-graph if it is an intersection graph of connected subgraphs of some subdivision of $H$. $H$-graphs naturally generalize several important graph classes like interval or circular-arc graph. This class…

Data Structures and Algorithms · Computer Science 2020-02-24 Fedor V. Fomin , Petr A. Golovach , Jean-Florent Raymond

We study the kernel complexity of constraint satisfaction problems over a finite domain, parameterized by the number of variables, whose constraint language consists of two relations: the non-equality relation and an additional…

Computational Complexity · Computer Science 2026-04-24 Ishay Haviv

A dominating set of a graph $G=(V,E)$ is a subset of vertices $S\subseteq V$ such that every vertex $v\in V\setminus S$ has at least one neighbor in set $S$. The corresponding optimization problem is known to be NP-hard. The best known…

Discrete Mathematics · Computer Science 2024-12-23 Ernesto Parra Inza , José María Sigarreta Almira , Nodari Vakhania

In the Shortest Superstring problem we are given a set of strings $S=\{s_1, \ldots, s_n\}$ and integer $\ell$ and the question is to decide whether there is a superstring $s$ of length at most $\ell$ containing all strings of $S$ as…

Data Structures and Algorithms · Computer Science 2015-02-06 Ivan Bliznets , Fedor V. Fomin , Petr A. Golovach , Nikolay Karpov , Alexander S. Kulikov , Saket Saurabh

In the F-minor-free deletion problem we want to find a minimum vertex set in a given graph that intersects all minor models of graphs from the family F. The Vertex planarization problem is a special case of F-minor-free deletion for the…

Data Structures and Algorithms · Computer Science 2022-02-07 Bart M. P. Jansen , Michał Włodarczyk

The paper develops a new technique to extract a characteristic subset from a random source that repeatedly samples from a set of elements. Here a characteristic subset is a set that when containing an element contains all elements that have…

Discrete Mathematics · Computer Science 2017-04-28 Pascal Schweitzer

We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)}…

Data Structures and Algorithms · Computer Science 2016-10-26 Dániel Marx , Marcin Pilipczuk

We introduce the cross-composition framework for proving kernelization lower bounds. A classical problem L AND/OR-cross-composes into a parameterized problem Q if it is possible to efficiently construct an instance of Q with polynomially…

Computational Complexity · Computer Science 2015-03-20 Hans L. Bodlaender , Bart M. P. Jansen , Stefan Kratsch

An edge dominating set of a graph G=(V,E) is a subset M of edges in the graph such that each edge in E-M is incident with at least one edge in M. In an instance of the parameterized edge dominating set problem we are given a graph G=(V,E)…

Discrete Mathematics · Computer Science 2011-04-22 Mingyu Xiao , Ton Kloks , Sheung-Hung Poon