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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

Given a directed graph $G$ and a list $(s_1,t_1),\dots,(s_d,t_d)$ of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of $G$ that contains a directed $s_i\to t_i$ path for every $1\le i \le k$. The…

Data Structures and Algorithms · Computer Science 2022-11-11 Andreas Emil Feldmann , Daniel Marx

The Planar Steiner Tree problem is one of the most fundamental NP-complete problems as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights, and a subset of vertices (often…

Data Structures and Algorithms · Computer Science 2018-11-19 Sándor Kisfaludi-Bak , Jesper Nederlof , Erik Jan van Leeuwen

In the Steiner Tree problem we are given an undirected edge-weighted graph as input, along with a set $K$ of vertices called terminals. The task is to output a minimum-weight connected subgraph that spans all the terminals. The famous…

Data Structures and Algorithms · Computer Science 2024-07-01 Bart M. P. Jansen , Céline M. F. Swennenhuis

A rectilinear Steiner tree for a set $P$ of points in $\mathbb{R}^2$ is a tree that connects the points in $P$ using horizontal and vertical line segments. The goal of Minimal Rectilinear Steiner Tree is to find a rectilinear Steiner tree…

Computational Geometry · Computer Science 2021-03-16 Henk Alkema , Mark de Berg

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

We study the multi-level Steiner tree problem: a generalization of the Steiner tree problem in graphs where terminals $T$ require varying priority, level, or quality of service. In this problem, we seek to find a minimum cost tree…

Data Structures and Algorithms · Computer Science 2020-05-18 Reyan Ahmed , Faryad Darabi Sahneh , Keaton Hamm , Stephen Kobourov , Richard Spence

The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…

Data Structures and Algorithms · Computer Science 2023-08-16 Cristina G. Fernandes , Carla N. Lintzmayer , Phablo F. S. Moura

We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph $G=(V,E,w)$, where $V=\{r\}\cup S \cup T$, and an integer $k$, the goal is to find a minimum cost subgraph of $G$ in which there are…

Data Structures and Algorithms · Computer Science 2024-07-11 Sarel Cohen , Lior Kamma , Aikaterini Niklanovits

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

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

Data Structures and Algorithms · Computer Science 2024-11-26 Antonios Antoniadis , Marek Eliáš , Adam Polak , Moritz Venzin

This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in…

Data Structures and Algorithms · Computer Science 2023-05-09 Dylan Hyatt-Denesik , Afrouz Jabal Ameli , Laura Sanità

In the rectilinear Steiner arborescence problem the task is to build a shortest rectilinear Steiner tree connecting a given root and a set of terminals which are placed in the plane such that all root-terminal-paths are shortest paths. This…

Computational Complexity · Computer Science 2015-08-28 Jens Maßberg

Given a metric space on n points, an {\alpha}-approximate universal algorithm for the Steiner tree problem outputs a distribution over rooted spanning trees such that for any subset X of vertices containing the root, the expected cost of…

Data Structures and Algorithms · Computer Science 2010-11-18 Anand Bhalgat , Deeparnab Chakrabarty , Sanjeev Khanna

In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…

Data Structures and Algorithms · Computer Science 2015-12-10 Stephan Beyer , Markus Chimani

The Steiner Forest problem is an important generalization of the Steiner Tree problem. We are given an undirected graph with nonnegative edge costs and a collection of pairs of vertices. The task is to compute a cheapest forest with the…

Data Structures and Algorithms · Computer Science 2024-12-10 Jarosław Byrka , Fabrizio Grandoni , Vera Traub

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

In this work we consider the Metric Steiner Forest problem in the sublinear time model. Given a set $V$ of $n$ points in a metric space where distances are provided by means of query access to an $n\times n$ distance matrix, along with a…

Data Structures and Algorithms · Computer Science 2025-10-14 Sepideh Mahabadi , Mohammad Roghani , Jakub Tarnawski , Ali Vakilian

We give a dynamic programming solution to find the minimum cost of a diameter constrained Steiner tree in case of directed graphs. Then we show a simple reduction from undirected version to the directed version to realize an algorithm of…

Data Structures and Algorithms · Computer Science 2021-10-20 Prashanth Amireddy , Chetan Sai Digumarthi

In the k-edge connected directed Steiner tree (k-DST) problem, we are given a directed graph G on n vertices with edge-costs, a root vertex r, a set of h terminals T and an integer k. The goal is to find a min-cost subgraph H of G that…

Data Structures and Algorithms · Computer Science 2016-03-01 Bundit Laekhanukit