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Graph parameters measure the amount of structure (or lack thereof) in a graph that makes it amenable to being decomposed in a way that facilitates dynamic programming. Graph decompositions and their associated parameters are important both…

Discrete Mathematics · Computer Science 2023-10-25 Svein Høgemo

We introduce merge-width, a family of graph parameters that unifies several structural graph measures, including treewidth, degeneracy, twin-width, clique-width, and generalized coloring numbers. Our parameters are based on new…

Combinatorics · Mathematics 2025-02-26 Jan Dreier , Szymon Toruńczyk

Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…

Discrete Mathematics · Computer Science 2024-11-20 Jessica Enright , Samuel D. Hand , Laura Larios-Jones , Kitty Meeks

We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…

Data Structures and Algorithms · Computer Science 2015-03-19 Stefan Szeider

We introduce a new framework for reconfiguration problems, and apply it to independent sets as the first example. Suppose that we are given an independent set $I_0$ of a graph $G$, and an integer $l \ge 0$ which represents a lower bound on…

Discrete Mathematics · Computer Science 2018-04-26 Takehiro Ito , Haruka Mizuta , Naomi Nishimura , Akira Suzuki

In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-08-07 Ran Ben-Basat , Ken-ichi Kawarabayashi , Gregory Schwartzman

We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give $n^{\mathcal{O}(w)}$-time algorithms on graphs of mim-width at…

Data Structures and Algorithms · Computer Science 2017-09-29 Lars Jaffke , O-joung Kwon , Jan Arne Telle

This paper settles the computational complexity of model checking of several extensions of the monadic second order (MSO) logic on two classes of graphs: graphs of bounded treewidth and graphs of bounded neighborhood diversity. A classical…

Computational Complexity · Computer Science 2026-01-06 Dušan Knop , Martin Koutecký , Tomáš Masařík , Tomáš Toufar

Algorithmic meta-theorems provide an important tool for showing tractability of graph problems on graph classes defined by structural restrictions. While such results are well established for static graphs, corresponding frameworks for…

Discrete Mathematics · Computer Science 2026-02-17 Michelle Döring , Jessica Enright , Laura Larios-Jones , George Skretas

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

Data Structures and Algorithms · Computer Science 2023-10-10 Siddharth Gupta , Guy Sa'ar , Meirav Zehavi

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

We present new refinement heuristics for the balanced graph partitioning problem that break with an age-old rule. Traditionally, local search only permits moves that keep the block sizes balanced (below a size constraint). In this work, we…

Social and Information Networks · Computer Science 2025-05-13 Nikolai Maas , Lars Gottesbüren , Daniel Seemaier

The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-18 Nicolas Bousquet , Laurent Feuilloley , Théo Pierron

A stable or locally-optimal cut of a graph is a cut whose weight cannot be increased by changing the side of a single vertex. In this paper we study Minimum Stable Cut, the problem of finding a stable cut of minimum weight. Since this…

Computational Complexity · Computer Science 2026-04-08 Michael Lampis

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

One of the central models in distributed computing is Linial's LOCAL model [SIAM J. Comp. 1992]. Over time, researchers have studied distributed graph problems in the LOCAL model under slightly different assumptions, such as whether nodes…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-14 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Timothé Picavet , Gustav Schmid

The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…

Data Structures and Algorithms · Computer Science 2018-12-10 Philipp Bamberger , Fabian Kuhn , Yannic Maus

A bipartite graph $G=(A,B,E)$ is ${\cal H}$-convex, for some family of graphs ${\cal H}$, if there exists a graph $H\in {\cal H}$ with $V(H)=A$ such that the set of neighbours in $A$ of each $b\in B$ induces a connected subgraph of $H$.…

Data Structures and Algorithms · Computer Science 2024-02-06 Flavia Bonomo-Braberman , Nick Brettell , Andrea Munaro , Daniël Paulusma

Many problems are known to be solvable in subexponential parameterized time when the input graph is planar. The bidimensionality framework of Demaine, Fomin, Hajiaghay, and Thilikos [JACM'05] and the treewidth-pattern-covering approach by…

Data Structures and Algorithms · Computer Science 2026-04-02 Matthias Bentert , Fedor V. Fomin , Petr A. Golovach

We continue the study of graph classes in which the treewidth can only be large due to the presence of a large clique, and, more specifically, of graph classes with bounded tree-independence number. In [Dallard, Milani\v{c}, and…

Data Structures and Algorithms · Computer Science 2022-09-27 Martin Milanič , Paweł Rzążewski