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We introduce graph width parameters, called $\alpha$-edge-crossing width and edge-crossing width. These are defined in terms of the number of edges crossing a bag of a tree-cut decomposition. They are motivated by edge-cut width, recently…

Data Structures and Algorithms · Computer Science 2025-07-31 Yeonsu Chang , O-joung Kwon , Myounghwan Lee

Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…

Computational Complexity · Computer Science 2007-05-23 Martin Grohe , Oleg Verbitsky

We prove that finding a $k$-edge induced subgraph is fixed-parameter tractable, thereby answering an open problem of Leizhen Cai. Our algorithm is based on several combinatorial observations, Gauss' famous \emph{Eureka} theorem [Andrews,…

Data Structures and Algorithms · Computer Science 2012-05-02 Bingkai Lin , Yijia Chen

We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le…

Data Structures and Algorithms · Computer Science 2013-10-02 Fedor V. Fomin , Petr A. Golovach , Janne H. Korhonen

We show that some natural problems that are XNLP-hard (which implies W[t]-hardness for all t) when parameterized by pathwidth or treewidth, become FPT when parameterized by stable gonality, a novel graph parameter based on optimal maps from…

Data Structures and Algorithms · Computer Science 2022-02-15 Hans L. Bodlaender , Gunther Cornelissen , Marieke van der Wegen

In this paper we study the complexity of the following problems: Given a colored graph X=(V,E,c), compute a minimum cardinality set S of vertices such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem…

Computational Complexity · Computer Science 2016-06-15 V. Arvind , Frank Fuhlbrück , Johannes Köbler , Sebastian Kuhnert , Gaurav Rattan

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…

Artificial Intelligence · Computer Science 2009-03-04 Christian Bessiere , Emmanuel Hebrard , Brahim Hnich , Zeynep Kiziltan , Toby Walsh

We give a fixed-parameter tractable (FPT) approximation algorithm computing the path-width of a tournament, and more generally, of a semi-complete digraph. Based on this result, we prove that topological containment and rooted immersion…

Data Structures and Algorithms · Computer Science 2012-08-03 Fedor V. Fomin , Michał Pilipczuk

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

To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…

Geometric Topology · Mathematics 2014-07-25 Benjamin A. Burton , William Pettersson

Treewidth is a graph parameter of fundamental importance to algorithmic and structural graph theory. This paper surveys several graph parameters tied to treewidth, including separation number, tangle number, well-linked number and Cartesian…

Combinatorics · Mathematics 2016-01-29 Daniel J. Harvey , David R. Wood

Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first…

Data Structures and Algorithms · Computer Science 2025-09-09 Joshua Könen , Heiko Röglin , Tarek Stuck

We study the parameterized complexity of the T(h+1)-Free Edge Deletion problem. Given a graph G and integers k and h, the task is to delete at most k edges so that every connected component of the resulting graph has size at most h. The…

Data Structures and Algorithms · Computer Science 2026-02-04 Ajinkya Gaikwad , Soumen Maity , Leeja R

We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently:…

Discrete Mathematics · Computer Science 2025-02-19 Hans L. Bodlaender , Carla Groenland , Hugo Jacob

Deciding feasibility of large systems of linear equations and inequalities is one of the most fundamental algorithmic tasks. However, due to data inaccuracies or modeling errors, in practical applications one often faces linear systems that…

Data Structures and Algorithms · Computer Science 2022-09-07 Kristóf Bérczi , Alexander Göke , Lydia Mirabel Mendoza-Cadena , Matthias Mnich

Many well-known NP-hard algorithmic problems on directed graphs resist efficient parametrisations with most known width measures for directed graphs, such as directed treewidth, DAG-width, Kelly-width and many others. While these focus on…

Discrete Mathematics · Computer Science 2019-05-31 Raphael Steiner , Sebastian Wiederrecht

Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components…

Data Structures and Algorithms · Computer Science 2024-04-29 Tesshu Hanaka , Michael Lampis , Manolis Vasilakis , Kanae Yoshiwatari

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…

Computational Geometry · Computer Science 2023-02-21 Sujoy Bhore , Robert Ganian , Liana Khazaliya , Fabrizio Montecchiani , Martin Nöllenburg

We revisit a graph width parameter that we dub bipartite treewidth (btw). Bipartite treewidth can be seen as a common generalization of treewidth and the odd cycle transversal number, and is closely related to odd-minors. Intuitively, a…

Data Structures and Algorithms · Computer Science 2025-12-01 Lars Jaffke , Laure Morelle , Ignasi Sau , Dimitrios M. Thilikos

We show an algorithm that, given an $n$-vertex graph $G$ and a parameter $k$, in time $2^{O(k \log k)} n^{O(1)}$ finds a tree decomposition of $G$ with the following properties: * every adhesion of the tree decomposition is of size at most…

Data Structures and Algorithms · Computer Science 2020-09-29 Marek Cygan , Paweł Komosa , Daniel Lokshtanov , Michał Pilipczuk , Marcin Pilipczuk , Saket Saurabh , Magnus Wahlström