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We show that the Minimal Length-Bounded L-But problem can be computed in linear time with respect to L and the tree-width of the input graph as parameters. In this problem the task is to find a set of edges of a graph such that after…

Data Structures and Algorithms · Computer Science 2016-10-25 Dušan Knop , Pavel Dvořák

Treewidth is a well-studied decompositional parameter to measure the tree-likeness of a graph. While the propositional satisfiability problem (SAT) is known to be tractable when parameterized by the treewidth of the underlying primal graph,…

Data Structures and Algorithms · Computer Science 2026-05-08 Robert Ganian , Marlene Gründel

Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a…

Data Structures and Algorithms · Computer Science 2018-09-05 Remie Janssen , Mark Jones , Steven Kelk , Georgios Stamoulis , Taoyang Wu

Many tractable algorithms for solving the Constraint Satisfaction Problem (CSP) have been developed using the notion of the treewidth of some graph derived from the input CSP instance. In particular, the incidence graph of the CSP instance…

Logic in Computer Science · Computer Science 2015-05-19 M. Praveen

Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge…

Data Structures and Algorithms · Computer Science 2023-07-11 Carla Binucci , Giuseppe Liotta , Fabrizio Montecchiani , Giacomo Ortali , Tommaso Piselli

Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…

Discrete Mathematics · Computer Science 2026-04-28 Jessica Enright , Samuel D. Hand , Laura Larios-Jones , Kitty Meeks

We associate a graph with a 1-safe Petri net and study the parameterized complexity of various problems with parameters derived from the graph. With treewidth as the parameter, we give W[1]-hardness results for many problems about 1-safe…

Logic in Computer Science · Computer Science 2011-06-13 M. Praveen , Kamal Lodaya

Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable…

Data Structures and Algorithms · Computer Science 2022-03-01 Cornelius Brand , Esra Ceylan , Christian Hatschka , Robert Ganian , Viktoriia Korchemna

We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva…

Data Structures and Algorithms · Computer Science 2022-07-20 Lars Jaffke , Paloma T. Lima , Daniel Lokshtanov

Temporal graphs are introduced to model systems where the relationships among the entities of the system evolve over time. In this paper, we consider the temporal graphs where the edge set changes with time and all the changes are known a…

Data Structures and Algorithms · Computer Science 2025-08-15 Rinku Kumar , Bodhisatwa Mazumdar , Subhrangsu Mandal

In the Directed Long Cycle Hitting Set} problem we are given a directed graph $G$, and the task is to find a set $S$ of at most $k$ vertices/arcs such that $G-S$ has no cycle of length longer than $\ell$. We show that the problem can be…

Data Structures and Algorithms · Computer Science 2020-03-12 Alexander Göke , Dániel Marx , Matthias Mnich

We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods across a cut of a graph. Boolean-width is similar to rank-width, which is related to the number of $GF[2]$-sums (1+1=0) of…

Data Structures and Algorithms · Computer Science 2011-03-10 B. -M. Bui-Xuan , J. A. Telle , M. Vatshelle

The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search where we are given a system of tunnels that is contaminated by…

Data Structures and Algorithms · Computer Science 2022-09-13 Mamadou Moustapha Kanté , Christophe Paul , Dimitrios M. Thilikos

One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms,…

Logic in Computer Science · Computer Science 2015-07-01 Stephan Kreutzer

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

Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…

Computational Complexity · Computer Science 2022-12-20 Falko Hegerfeld , Stefan Kratsch

Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…

Discrete Mathematics · Computer Science 2025-09-29 Mehul Bafna , Shaghik Amirian

We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…

Data Structures and Algorithms · Computer Science 2018-12-18 Michael J. Bannister , Sergio Cabello , David Eppstein

Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…

Data Structures and Algorithms · Computer Science 2014-04-30 Yoichi Iwata , Keigo Oka

We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as…

Data Structures and Algorithms · Computer Science 2022-07-18 Fedor V. Fomin , Petr A. Golovach , Tuukka Korhonen , Kirill Simonov , Giannos Stamoulis