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Related papers: The bottleneck 2-connected $k$-Steiner network pro…

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Network flow interdiction analysis studies by how much the value of a maximum flow in a network can be diminished by removing components of the network constrained to some budget. Although this problem is strongly NP-complete on general…

Discrete Mathematics · Computer Science 2008-01-14 Rico Zenklusen

The starting point of our work is a decade-old open question concerning the subexponential parameterized complexity of \textsc{2-Layer Crossing Minimization}. In this problem, the input is an $n$-vertex graph $G$ whose vertices are…

Data Structures and Algorithms · Computer Science 2025-10-16 Fedor V. Fomin , Petr A. Golovach , Tanmay Inamdar , Saket Saurabh , Meirav Zehavi

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

In the k-2VC problem, we are given an undirected graph G with edge costs and an integer k; the goal is to find a minimum-cost 2-vertex-connected subgraph of G containing at least k vertices. A slightly more general version is obtained if…

Data Structures and Algorithms · Computer Science 2008-02-19 Chandra Chekuri , Nitish Korula

The Steiner Multicut problem asks, given an undirected graph G, terminals sets T1,...,Tt $\subseteq$ V(G) of size at most p, and an integer k, whether there is a set S of at most k edges or nodes s.t. of each set Ti at least one pair of…

Data Structures and Algorithms · Computer Science 2015-06-24 Karl Bringmann , Danny Hermelin , Matthias Mnich , Erik Jan van Leeuwen

Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected…

Data Structures and Algorithms · Computer Science 2017-05-31 Shiri Chechik , Thomas Dueholm Hansen , Giuseppe F. Italiano , Veronika Loitzenbauer , Nikos Parotsidis

Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call $h$-Clique2Path Planarity: Given a graph $G$, whose vertices are partitioned into subsets of size at most $h$, each…

Data Structures and Algorithms · Computer Science 2018-08-29 Patrizio Angelini , Peter Eades , Seok-Hee Hong , Karsten Klein , Stephen Kobourov , Giuseppe Liotta , Alfredo Navarra , Alessandra Tappini

For all integers $k\geq 3$, we give an $O(n^4)$ time algorithm for the problem whose instance is a graph $G$ of girth at least $k$ together with $k$ vertices and whose question is "Does $G$ contains an induced subgraph containing the $k$…

Discrete Mathematics · Computer Science 2013-09-06 Wei Liu , Nicolas Trotignon

We study connectivity problems from a fine-grained parameterized perspective. Cygan et al. (TALG 2022) obtained algorithms with single-exponential running time $\alpha^{tw} n^{O(1)}$ for connectivity problems parameterized by treewidth…

Data Structures and Algorithms · Computer Science 2023-03-01 Falko Hegerfeld , Stefan Kratsch

This paper optimizes path planning for a trunkand-branch topology network in an irregular 2-dimensional manifold embedded in 3-dimensional Euclidean space with application to submarine cable network planning. We go beyond our earlier focus…

Systems and Control · Electrical Eng. & Systems 2022-01-19 Tianjiao Wang , Zengfu Wang , Bill Moran , Moshe Zukerman

We consider minimum-cardinality Manhattan connected sets with arbitrary demands: Given a collection of points $P$ in the plane, together with a subset of pairs of points in $P$ (which we call demands), find a minimum-cardinality superset of…

Data Structures and Algorithms · Computer Science 2020-10-28 Antonios Antoniadis , Margarita Capretto , Parinya Chalermsook , Christoph Damerius , Peter Kling , Lukas Nölke , Nidia Obscura , Joachim Spoerhase

In this paper, we design a framework to obtain efficient algorithms for several problems with a global constraint (acyclicity or connectivity) such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest…

Data Structures and Algorithms · Computer Science 2023-10-10 Benjamin Bergougnoux , Mamadou Moustapha Kanté

Let v(G) be the number of vertices and t(G,k) the maximum number of disjoint k-edge trees in G. In this paper we show that (a1) if G is a graph with every vertex of degree at least two and at most s, where s > 3, then t(G,2) is at least…

Combinatorics · Mathematics 2007-05-23 Alexander Kelmans

We study the Steiner Tree problem on the intersection graph of most natural families of geometric objects, e.g., disks, squares, polygons, etc. Given a set of $n$ objects in the plane and a subset $T$ of $t$ terminal objects, the task is to…

Computational Geometry · Computer Science 2025-11-11 Sujoy Bhore , Baris Can Esmer , Daniel Marx , Karol Wegrzycki

In the spanning-tree congestion problem ($\mathsf{STC}$), we are given a graph $G$, and the objective is to compute a spanning tree of $G$ that minimizes the maximum edge congestion. While $\mathsf{STC}$ is known to be $\mathbb{NP}$-hard,…

Data Structures and Algorithms · Computer Science 2026-02-12 Sunny Atalig , Marek Chrobak , Christoph Dürr , Petr Kolman , Huong Luu , Jiří Sgall , Gregory Zhu

The graph parameters highway dimension and skeleton dimension were introduced to capture the properties of transportation networks. As many important optimization problems like Travelling Salesperson, Steiner Tree or $k$-Center arise in…

Discrete Mathematics · Computer Science 2019-11-20 Johannes Blum

For the well-known Survivable Network Design Problem (SNDP) we are given an undirected graph $G$ with edge costs, a set $R$ of terminal vertices, and an integer demand $d_{s,t}$ for every terminal pair $s,t\in R$. The task is to compute a…

Data Structures and Algorithms · Computer Science 2022-11-09 Andreas Emil Feldmann , Anish Mukherjee , Erik Jan van Leeuwen

We study Steiner Forest on $H$-subgraph-free graphs, that is, graphs that do not contain some fixed graph $H$ as a (not necessarily induced) subgraph. We are motivated by a recent framework that completely characterizes the complexity of…

We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…

Combinatorics · Mathematics 2019-07-04 Abdel-Rahman Madkour , Phillip Nadolny , Matthew Wright

Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…

Computational Geometry · Computer Science 2014-12-04 Matthias Henze , Rafel Jaume