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A graph is geometric 1-planar if it admits a straight-line drawing where each edge is crossed at most once. We provide the first systematic study of the parameterized complexity of recognizing geometric 1-planar graphs. By substantially…

Computational Complexity · Computer Science 2026-02-11 Alexander Firbas

We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also…

Data Structures and Algorithms · Computer Science 2026-02-19 Pavel Dvořák , Andreas Emil Feldmann , Dušan Knop , Tomáš Masařík , Tomáš Toufar , Pavel Veselý

Given an $n\times n\times p$ cost array $C$ we consider the problem $p$-P3AP which consists in finding $p$ pairwise disjoint permutations $\varphi_1,\varphi_2,\ldots,\varphi_p$ of $\{1,\ldots,n\}$ such that…

Optimization and Control · Mathematics 2014-05-21 Ante Ćustić , Bettina Klinz , Gerhard J. Woeginger

We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem. In particular, we provide fixed parameter tractable algorithms…

Computational Geometry · Computer Science 2013-09-02 Michael J. Bannister , David Eppstein , Joseph A. Simons

We consider problems that can be formulated as a task of finding an optimal triangulation of a graph w.r.t. some notion of optimality. We present algorithms parameterized by the size of a minimum edge clique cover ($cc$) to such problems.…

Data Structures and Algorithms · Computer Science 2022-02-08 Tuukka Korhonen

In a recent paper, {\it Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (II)}, we discussed two algorithms for deforming and contracting a simply connected discrete closed manifold into a discrete sphere.…

Geometric Topology · Mathematics 2020-02-12 Li Chen

The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…

Discrete Mathematics · Computer Science 2017-07-10 Stephan Kreutzer , Patrice Ossona de Mendez , Roman Rabinovich , Sebastian Siebertz

Continuing results from JCDCGGG 2016 and 2017, we solve several new cases of the simple foldability problem -- deciding which crease patterns can be folded flat by a sequence of (some model of) simple folds. We give new efficient algorithms…

Computational Geometry · Computer Science 2023-06-02 Hugo Akitaya , Josh Brunner , Erik D. Demaine , Dylan Hendrickson , Victor Luo , Andy Tockman

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

This paper studies the computational complexity of the Edge Packing problem and the Vertex Packing problem. The edge packing problem (denoted by $\bar{EDS}$) and the vertex packing problem (denoted by $\bar{DS} $) are linear programming…

Computational Complexity · Computer Science 2011-04-08 Sameera Muhamed Salam , K. N. Parvathy , K. S. Sudeep , K. Murali Krishnan

The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts the performance of the SBBU algorithm for protein structure…

Data Structures and Algorithms · Computer Science 2025-12-04 Michael Souza , Júlio Araújo , John Kesley Costa , Carlile Lavor

In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…

Computational Complexity · Computer Science 2012-01-18 Sepp Hartung , André Nichterlein

In this paper we study the Spanning Tree Congestion problem, where we are given a graph $G=(V,E)$ and are asked to find a spanning tree $T$ of minimum maximum congestion. Here, the congestion of an edge $e\in T$ is the number of edges…

Data Structures and Algorithms · Computer Science 2026-05-28 Michael Lampis , Valia Mitsou , Edouard Nemery , Yota Otachi , Manolis Vasilakis , Daniel Vaz

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 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

We study the problem of connecting the parts of a multipartite graph using a minimum number of edges under a matching constraint. We introduce interconnection trees, defined as matchings whose projections onto the quotient graph form a…

Computational Complexity · Computer Science 2026-05-19 Noé Demange , Yann Strozecki

The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…

Computational Complexity · Computer Science 2016-11-24 Carolin Albrecht , Frank Gurski , Jochen Rethmann , Eda Yilmaz

Genome rearrangement is a common model for molecular evolution. In this paper, we consider the Pairwise Rearrangement problem, which takes as input two genomes and asks for the number of minimum-length sequences of permissible operations…

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

Data Structures and Algorithms · Computer Science 2022-09-27 Marin Bougeret , Jérémy Omer , Michael Poss

This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph $G$ and a set of terminal pairs $P$ and asks whether $G$ contains a set of pairwise edge-disjoint paths connecting every terminal…

Data Structures and Algorithms · Computer Science 2018-08-13 Robert Ganian , Sebastian Ordyniak