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Related papers: Parameterized Algorithms for Modular-Width

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In this work, we study two natural generalizations of clique-width introduced by Martin F\"urer. Multi-clique-width (mcw) allows every vertex to hold multiple labels [ITCS 2017], while for fusion-width (fw) we have a possibility to merge…

Data Structures and Algorithms · Computer Science 2023-07-11 Vera Chekan , Stefan Kratsch

Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…

Combinatorics · Mathematics 2025-07-24 Vilhelm Agdur , Jessica Enright , Laura Larios-Jones , Kitty Meeks , Fiona Skerman , Ella Yates

While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…

Computational Complexity · Computer Science 2024-12-02 Shreya Gupta , Boyang Huang , Russell Impagliazzo , Stanley Woo , Christopher Ye

We investigate a structural generalisation of treewidth we call $\mathcal{A}$-blind-treewidth where $\mathcal{A}$ denotes an annotated graph class. This width parameter is defined by evaluating only the size of those bags $B$ of…

Combinatorics · Mathematics 2024-10-03 J. Pascal Gollin , Sebastian Wiederrecht

Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…

Data Structures and Algorithms · Computer Science 2021-02-12 Ajinkya Gaikwad , Soumen Maity

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…

Data Structures and Algorithms · Computer Science 2007-11-20 Binh-Minh Bui-Xuan , Michel Habib , Vincent Limouzy , Fabien De Montgolfier

The Firefighting problem is defined as follows. At time $t=0$, a fire breaks out at a vertex of a graph. At each time step $t \geq 0$, a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all…

Data Structures and Algorithms · Computer Science 2017-11-29 Bireswar Das , Murali Krishna Enduri , Neeldhara Misra , I. Vinod Reddy

The generic homomorphism problem, which asks whether an input graph $G$ admits a homomorphism into a fixed target graph $H$, has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of…

Computational Complexity · Computer Science 2022-10-14 Robert Ganian , Thekla Hamm , Viktoriia Korchemna , Karolina Okrasa , Kirill Simonov

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 investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…

Discrete Mathematics · Computer Science 2023-09-22 Hans L. Bodlaender , Carla Groenland , Michał Pilipczuk

We investigate two types of graph layouts, track layouts and layered path decompositions, and the relations between their associated parameters track-number and layered pathwidth. We use these two types of layouts to characterize leveled…

Combinatorics · Mathematics 2019-04-10 Michael J. Bannister , William E. Devanny , Vida Dujmović , David Eppstein , David R. Wood

Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…

Combinatorics · Mathematics 2022-12-22 Colin McDiarmid , Fiona Skerman

We study the parameterized and kernelization complexity of the s-Club Cluster Edge Deletion problem, a distance-bounded generalization of Cluster Edge Deletion. Given a graph G = (V, E) and integers k and s, the goal is to delete at most k…

Discrete Mathematics · Computer Science 2025-11-04 Ajinkya Gaikwad

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

Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and…

Data Structures and Algorithms · Computer Science 2026-05-22 Shiva Kintali , Nishad Kothari , Akash Kumar

Control-flow graphs (CFGs) of structured programs are well known to exhibit strong sparsity properties. Traditionally, this sparsity has been modeled using graph parameters such as treewidth and pathwidth, enabling the development of faster…

Programming Languages · Computer Science 2026-02-10 Xuran Cai , Amir Goharshady , S Hitarth , Chun Kit Lam

We study the kernelization complexity of structural parameterizations of the Vertex Cover problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce any instance $(G,k)$ of the Vertex Cover problem to an…

Data Structures and Algorithms · Computer Science 2023-07-25 Marin Bougeret , Bart M. P. Jansen , Ignasi Sau

Although it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this paper, we give FPT algorithms for the…

Data Structures and Algorithms · Computer Science 2020-06-09 Arman Boyacı , Tınaz Ekim , Mordechai Shalom

In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we…

Data Structures and Algorithms · Computer Science 2026-05-21 Mateus de Oliveira Oliveira , Sam Urmian

There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…

Data Structures and Algorithms · Computer Science 2017-10-24 Yoichi Iwata , Tomoaki Ogasawara , Naoto Ohsaka