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A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.…

Data Structures and Algorithms · Computer Science 2023-06-22 Louis Dublois , Michael Lampis , Vangelis Th. Paschos

We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…

Data Structures and Algorithms · Computer Science 2024-10-23 Robert Ganian , Mathis Rocton , Daniel Unterberger

We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k…

Data Structures and Algorithms · Computer Science 2018-04-24 Ivona Bezáková , Radu Curticapean , Holger Dell , Fedor V. Fomin

We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…

Data Structures and Algorithms · Computer Science 2022-06-24 Mahdi Belbasi , Martin Fürer

Tree-width has been proven to be a useful parameter to design fast and efficient algorithms for intractable problems. However, while tree-width is low on relatively sparse graphs can be arbitrary high on dense graphs. Therefore, we…

Data Structures and Algorithms · Computer Science 2021-11-04 Chris Aronis

While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of…

Logic in Computer Science · Computer Science 2020-04-07 Onur Çağırıcı , Petr Hliněný , Filip Pokrývka , Abhisekh Sankaran

Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general…

Combinatorics · Mathematics 2021-12-23 Konrad K. Dabrowski , Matthew Johnson , Daniël Paulusma

Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions. Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we…

Data Structures and Algorithms · Computer Science 2020-04-29 Till Fluschnik , Hendrik Molter , Rolf Niedermeier , Malte Renken , Philipp Zschoche

We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint…

Discrete Mathematics · Computer Science 2024-01-04 Miguel Romero , Marcin Wrochna , Stanislav Živný

We investigate the parameterized complexity of the Isometric Path Partition problem when parameterized by the treewidth ($\mathrm{tw}$) of the input graph, arguably one of the most widely studied parameters. Courcelle's theorem shows that…

Data Structures and Algorithms · Computer Science 2025-09-23 Dibyayan Chakraborty , Oscar Defrain , Florent Foucaud , Mathieu Mari , Prafullkumar Tale

We combine ideas from distance sensitivity oracles (DSOs) and fixed-parameter tractability (FPT) to design sensitivity oracles for FPT graph problems. An oracle with sensitivity $f$ for an FPT problem $\Pi$ on a graph $G$ with parameter $k$…

Data Structures and Algorithms · Computer Science 2021-12-07 Davide Bilò , Katrin Casel , Keerti Choudhary , Sarel Cohen , Tobias Friedrich , J. A. Gregor Lagodzinski , Martin Schirneck , Simon Wietheger

Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph $G$ into node-disjoint subgraphs, where each subgraph has sufficiently large…

Data Structures and Algorithms · Computer Science 2013-04-08 Chandra Chekuri , Julia Chuzhoy

We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…

Discrete Mathematics · Computer Science 2015-12-04 Jiří Fiala , Tomáš Gavenčiak , Dušan Knop , Martin Koutecký , Jan Kratochvíl

We study "space efficient" FPT algorithms for graph problems with limited memory. Let n be the size of the input graph and k be the parameter. We present algorithms that run in time f(k)*poly(n) and use g(k)*polylog(n) working space, where…

Data Structures and Algorithms · Computer Science 2025-12-16 Sheikh Shakil Akhtar , Pranabendu Misra , Geevarghese Philip

Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property…

Combinatorics · Mathematics 2024-02-21 Bogdan Alecu , Mamadou Moustapha Kanté , Vadim Lozin , Viktor Zamaraev

The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47-66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequate than treewidth as an…

Data Structures and Algorithms · Computer Science 2018-05-16 Eunjung Kim , Sang-il Oum , Christophe Paul , Ignasi Sau , Dimitrios M. Thilikos

We develop a framework for applying treewidth-based dynamic programming on graphs with "hybrid structure", i.e., with parts that may not have small treewidth but instead possess other structural properties. Informally, this is achieved by…

Data Structures and Algorithms · Computer Science 2019-08-28 Eduard Eiben , Robert Ganian , Thekla Hamm , O-joung Kwon

We describe a polynomial-time algorithm which, given a graph $G$ with treewidth $t$, approximates the pathwidth of $G$ to within a ratio of $O(t\sqrt{\log t})$. This is the first algorithm to achieve an $f(t)$-approximation for some…

Data Structures and Algorithms · Computer Science 2023-03-13 Carla Groenland , Gwenaël Joret , Wojciech Nadara , Bartosz Walczak

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…

Computational Complexity · Computer Science 2021-01-06 Archontia C. Giannopoulou , George B. Mertzios , Rolf Niedermeier

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