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The Euclidean Steiner tree problem seeks the min-cost network to connect a collection of target locations, and it underlies many applications of wireless networks. In this paper, we present a study on solving the Euclidean Steiner tree…

Machine Learning · Computer Science 2022-09-22 Siqi Wang , Yifan Wang , Guangmo Tong

Given two sets of points in the plane, $P$ of $n$ terminals and $S$ of $m$ Steiner points, a Steiner tree of $P$ is a tree spanning all points of $P$ and some (or none or all) points of $S$. A Steiner tree with length of longest edge…

Computational Geometry · Computer Science 2010-12-08 A. Karim Abu-Affash

Bottleneck Steiner networks model energy consumption in wireless ad-hoc networks. The task is to design a network spanning a given set of terminals and at most $k$ Steiner points such that the length of the longest edge is minimised. The…

Combinatorics · Mathematics 2019-07-09 M Brazil , C Ras , D Thomas , G Xu

The Euclidean Steiner tree problem, normally posed in two dimensions, seeks to connect a set of prescribed terminal nodes by placing additional nodes, known as Steiner points, with edges connecting such nodes either to another Steiner point…

Systems and Control · Electrical Eng. & Systems 2026-04-24 Manou Rosenberg , Mengbin Ye , Brian D. O. Anderson

We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…

Networking and Internet Architecture · Computer Science 2018-03-14 Magnus M. Halldorsson , Guy Kortsarz , Pradipta Mitra , Tigran Tonoyan

We consider an important generalization of the Steiner tree problem, the \emph{Steiner forest problem}, in the Euclidean plane: the input is a multiset $X \subseteq \mathbb{R}^2$, partitioned into $k$ color classes $C_1, C_2, \ldots, C_k…

Data Structures and Algorithms · Computer Science 2024-05-14 Artur Czumaj , Shaofeng H. -C. Jiang , Robert Krauthgamer , Pavel Veselý

The geometric bottleneck Steiner network problem on a set of vertices $X$ embedded in a normed plane requires one to construct a graph $G$ spanning $X$ and a variable set of $k\geq 0$ additional points, such that the length of the longest…

Combinatorics · Mathematics 2013-01-22 M. Brazil , C. J. Ras , D. A. Thomas

We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network…

Data Structures and Algorithms · Computer Science 2017-07-12 Guru Guruganesh , Jennifer Iglesias , R. Ravi , Laura Sanità

We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…

Data Structures and Algorithms · Computer Science 2015-08-19 Jens Maßberg

The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…

Data Structures and Algorithms · Computer Science 2023-08-24 Swati Gupta , Ali Khodabakhsh , Hassan Mortagy , Evdokia Nikolova

Motivated by hierarchical networks, we introduce the Flow-weighted Layered Metric Euclidean Capacitated Steiner Tree (FLaMECaST) problem, a variant of the Euclidean Steiner tree with layered structure and capacity constraints per layer. The…

Data Structures and Algorithms · Computer Science 2025-08-28 Thomas Bläsius , Henrik Csöre , Max Göttlicher , Elly Schmidt , Wendy Yi

The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear…

Computational Geometry · Computer Science 2023-12-01 T-H. Hubert Chan , Gramoz Goranci , Shaofeng H. -C. Jiang , Bo Wang , Quan Xue

Greedy embedding (or drawing) is a simple and efficient strategy to route messages in wireless sensor networks. For each source-destination pair of nodes s, t in a greedy embedding there is always a neighbor u of s that is closer to t…

Computational Geometry · Computer Science 2013-06-24 Martin Nöllenburg , Roman Prutkin

In the classical (min-cost) Steiner tree problem, we are given an edge-weighted undirected graph and a set of terminal nodes. The goal is to compute a min-cost tree S which spans all terminals. In this paper we consider the min-power…

Data Structures and Algorithms · Computer Science 2012-05-17 Fabrizio Grandoni

We propose a novel relay augmentation strategy for extending the lifetime of a certain class of wireless sensor networks. In this class sensors are located at fixed and pre-determined positions and all communication takes place via…

Optimization and Control · Mathematics 2013-10-22 Marcus Brazil , Charl Ras , Doreen Thomas

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

Let $P$ and $S$ be two disjoint sets of $n$ and $m$ points in the plane, respectively. We consider the problem of computing a Steiner tree whose Steiner vertices belong to $S$, in which each point of $P$ is a leaf, and whose longest edge…

Computational Geometry · Computer Science 2013-05-02 Ahmad Biniaz , Anil Maheshwari , Michiel Smid

The Euclidean Steiner problem is the problem of finding a set $St$, with the shortest length, such that $St \cup A$ is connected, where $A$ is a given set in a Euclidean space. The solutions $St$ to the Steiner problem will be called…

Metric Geometry · Mathematics 2025-02-20 Danila Cherkashin , Emanuele Paolini , Yana Teplitskaya

We introduce a new variant of the geometric Steiner arborescence problem, motivated by the layout of flow maps. Flow maps show the movement of objects between places. They reduce visual clutter by bundling lines smoothly and avoiding…

Computational Geometry · Computer Science 2011-09-16 Kevin Buchin , Bettina Speckmann , Kevin Verbeek

In the Euclidean Steiner Tree problem, we are given as input a set of points (called terminals) in the $\ell_2$-metric space and the goal is to find the minimum-cost tree connecting them. Additional points (called Steiner points) from the…

Combinatorics · Mathematics 2023-12-05 Henry Fleischmann , Guillermo A. Gamboa Q. , Karthik C. S. , Josef Matějka , Jakub Petr
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