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The width measure \emph{treedepth}, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. We present an algorithm which---given as input…

Data Structures and Algorithms · Computer Science 2014-08-21 Felix Reidl , Peter Rossmanith , Fernando Sanchez Villaamil , Somnath Sikdar

Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…

Logic in Computer Science · Computer Science 2018-01-17 Jouke Witteveen , Leen Torenvliet

Compatibility of unrooted phylogenetic trees is a well studied problem in phylogenetics. It asks to determine whether for a set of k input trees there exists a larger tree (called a supertree) that contains the topologies of all k input…

Discrete Mathematics · Computer Science 2014-03-03 Alexander Grigoriev , Steven Kelk , Nela Lekic

In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the…

Data Structures and Algorithms · Computer Science 2022-12-06 Thomas Erlebach , Jakob T. Spooner

In this paper, we study the problem of minimizing a polynomial function with literals over all binary points, often referred to as pseudo-Boolean optimization. We investigate the fundamental limits of computation for this problem by…

Optimization and Control · Mathematics 2025-02-03 Alberto Del Pia , Aida Khajavirad

In the Fully Leafed Induced Subtrees, one is given a graph $G$ and two integers $a$ and $b$ and the question is to find an induced subtree of $G$ with $a$ vertices and at least $b$ leaves. This problem is known to be NP-complete even when…

Data Structures and Algorithms · Computer Science 2026-04-08 Julien Baste

We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at…

Data Structures and Algorithms · Computer Science 2015-06-30 Danny Hermelin , Moshe Kaspi , Christian Komusiewicz , Barak Navon

General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…

Discrete Mathematics · Computer Science 2024-05-24 Shuai Shao , Stanislav Živný

The Cut & Count technique and the rank-based approach have lead to single-exponential FPT algorithms parameterized by treewidth, that is, running in time $2^{O(tw)}n^{O(1)}$, for Feedback Vertex Set and connected versions of the classical…

Data Structures and Algorithms · Computer Science 2020-07-29 Benjamin Bergougnoux , Édouard Bonnet , Nick Brettell , O-joung Kwon

The clique-width is a measure of complexity of decomposing graphs into certain tree-like structures. The class of graphs with bounded clique-width contains bounded tree-width graphs. We give a polynomial time graph isomorphism algorithm for…

Computational Complexity · Computer Science 2016-04-29 Bireswar Das , Murali Krishna Enduri , I. Vinod Reddy

We show that the dominating set problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K(1,3)), the complete bipartite graph on four vertices where the two parts have one and three…

Data Structures and Algorithms · Computer Science 2015-03-17 Marek Cygan , Geevarghese Philip , Marcin Pilipczuk , Michał Pilipczuk , Jakub Onufry Wojtaszczyk

Several different measures for digraph width have appeared in the last few years. However, none of them shares all the "nice" properties of treewidth: First, being \emph{algorithmically useful} i.e. admitting polynomial-time algorithms for…

Discrete Mathematics · Computer Science 2016-08-14 Robert Ganian , Petr Hliněný , Joachim Kneis , Daniel Meister , Jan Obdržálek , Peter Rossmanith , Somnath Sikdar

Recently, Bumpus and Meeks introduced a purely temporal parameter, called vertex-interval-membership-width, which is promising for the design of fixed-parameter tractable (FPT) algorithms for vertex reachability problems in temporal graphs.…

Computational Complexity · Computer Science 2025-07-09 Justine Cauvi , Laurent Viennot

The notion of directed treewidth was introduced by Johnson, Robertson, Seymour and Thomas [Journal of Combinatorial Theory, Series B, Vol 82, 2001] as a first step towards an algorithmic metatheory for digraphs. They showed that some…

Data Structures and Algorithms · Computer Science 2015-10-09 Mateus de Oliveira Oliveira

We present a fixed-parameter tractable algorithm for first-order model checking on interpretations of graph classes with bounded local cliquewidth. Notably, this includes interpretations of planar graphs, and more generally, of classes of…

Data Structures and Algorithms · Computer Science 2022-03-01 Édouard Bonnet , Jan Dreier , Jakub Gajarský , Stephan Kreutzer , Nikolas Mählmann , Pierre Simon , Szymon Toruńczyk

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every…

Data Structures and Algorithms · Computer Science 2015-03-17 Dániel Marx , Igor Razgon

In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The…

Optimization and Control · Mathematics 2022-11-30 D. V. Gribanov , D. S. Malyshev , P. M. Pardalos , S. I. Veselov

There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…

Artificial Intelligence · Computer Science 2012-12-12 Yong Gao

A circle graph is the intersection graph of a set of chords in a circle. Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that Dominating Set, Connected Dominating Set, and Total Dominating Set are NP-complete in circle graphs.…

Data Structures and Algorithms · Computer Science 2012-05-17 Nicolas Bousquet , Daniel Gonçalves , George B. Mertzios , Christophe Paul , Ignasi Sau , Stéphan Thomassé

Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and QUANTIFIED SAT or, more generally, QUANTIFIED CSP, are FPT…

Computational Complexity · Computer Science 2025-03-18 Florent Foucaud , Esther Galby , Liana Khazaliya , Shaohua Li , Fionn Mc Inerney , Roohani Sharma , Prafullkumar Tale