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Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…

Data Structures and Algorithms · Computer Science 2024-01-22 Huairui Chu , Bingkai Lin

We study parameterized and approximation algorithms for a variant of Set Cover, where the universe of elements to be covered consists of points in the plane and the sets with which the points should be covered are segments. We call this…

Computational Geometry · Computer Science 2024-02-27 Katarzyna Kowalska , Michał Pilipczuk

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

We study extensions of the classic \emph{Line Cover} problem, which asks whether a set of $n$ points in the plane can be covered using $k$ lines. Line Cover is known to be NP-hard, and we focus on two natural generalizations. The first is…

Computational Geometry · Computer Science 2026-03-26 Matthias Bentert , Fedor v. Fomin , Petr A. Golovach , Souvik Saha , Sanjay Seetharaman , Kirill Simonov , Anannya Upasana

A matching is a set of edges in a graph with no common endpoint. A matching M is called acyclic if the induced subgraph on the endpoints of the edges in M is acyclic. Given a graph G and an integer k, Acyclic Matching Problem seeks for an…

Computational Complexity · Computer Science 2022-10-05 Sahab Hajebi , Ramin Javadi

A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…

Computational Complexity · Computer Science 2026-05-05 Christian Komusiewicz , Nils Morawietz , Frank Sommer , Luca Pascal Staus

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique…

Computational Complexity · Computer Science 2015-11-30 Abbas Bazzi , Samuel Fiorini , Sebastian Pokutta , Ola Svensson

The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…

Data Structures and Algorithms · Computer Science 2015-03-19 Gregory Gutin , Eun Jung Kim , Arezou Soleimanfallah , Stefan Szeider , Anders Yeo

This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…

Symbolic Computation · Computer Science 2013-10-04 Tatsuya Akutsu , Takeyuki Tamura , Atsuhiro Takasu

For intractable problems on graphs of bounded treewidth, two graph parameters treedepth and vertex cover number have been used to obtain fine-grained complexity results. Although the studies in this direction are successful, we still need a…

Data Structures and Algorithms · Computer Science 2023-04-03 Tatsuya Gima , Tesshu Hanaka , Masashi Kiyomi , Yasuaki Kobayashi , Yota Otachi

In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an…

Data Structures and Algorithms · Computer Science 2023-02-02 Leon Kellerhals , Tomohiro Koana , Pascal Kunz , Rolf Niedermeier

Computing planar orthogonal drawings with the minimum number of bends is one of the most relevant topics in Graph Drawing. The problem is known to be NP-hard, even when we want to test the existence of a rectilinear planar drawing, i.e., an…

Computational Geometry · Computer Science 2023-09-07 Emilio Di Giacomo , Walter Didimo , Giuseppe Liotta , Fabrizio Montecchiani , Giacomo Ortali

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…

Data Structures and Algorithms · Computer Science 2022-06-03 Robert Ganian , Eun Jung Kim , Stefan Szeider

Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…

Data Structures and Algorithms · Computer Science 2008-02-14 Omid Amini , Fedor V. Fomin , Saket Saurabh

The NP-hard Metric Dimension problem is to decide for a given graph G and a positive integer k whether there is a vertex subset of size at most k that separates all vertex pairs in G. Herein, a vertex v separates a pair {u,w} if the…

Computational Complexity · Computer Science 2012-11-08 Sepp Hartung , André Nichterlein

We study the parameterized complexity of the T(h+1)-Free Edge Deletion problem. Given a graph G and integers k and h, the task is to delete at most k edges so that every connected component of the resulting graph has size at most h. The…

Data Structures and Algorithms · Computer Science 2026-02-04 Ajinkya Gaikwad , Soumen Maity , Leeja R

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

We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…

Computational Complexity · Computer Science 2014-01-14 Jiong Guo , Yash Raj Shrestha

In Terminal Monitoring Set (TMS), the input is an undirected graph $G=(V,E)$, together with a collection $T$ of terminal pairs and the goal is to find a subset $S$ of minimum size that hits a shortest path between every pair of terminals.…

Discrete Mathematics · Computer Science 2024-06-05 N. R. Aravind , Roopam Saxena

A graph vertex-subset problem defines which subsets of the vertices of an input graph are feasible solutions. We view a feasible solution as a set of tokens placed on the vertices of the graph. A reconfiguration variant of a vertex-subset…

Computational Complexity · Computer Science 2022-04-25 Nicolas Bousquet , Amer E. Mouawad , Naomi Nishimura , Sebastian Siebertz