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In the Priority Steiner Tree (PST) problem, we are given an undirected graph $G=(V,E)$ with a source $s \in V$ and terminals $T \subseteq V \setminus \{s\}$, where each terminal $v \in T$ requires a nonnegative priority $P(v)$. The goal is…

Data Structures and Algorithms · Computer Science 2021-09-01 Faryad Darabi Sahneh , Stephen Kobourov , Richard Spence

For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time…

Data Structures and Algorithms · Computer Science 2013-07-18 Bang Ye Wu

{\em Reoptimization} is a setting in which we are given an (near) optimal solution of a problem instance and a local modification that slightly changes the instance. The main goal is that of finding an (near) optimal solution of the…

Data Structures and Algorithms · Computer Science 2018-05-01 Davide Bilò

The Prize-Collecting Steiner Tree (PCST) problem is a generalization of the Steiner Tree problem that has applications in network design, content distribution networks, and many more. There are a few centralized approximation algorithms…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-02-21 Parikshit Saikia , Sushanta Karmakar , Aris T. Pagourtzis

We give a 1.25 approximation algorithm for the Steiner Tree Problem with distances one and two, improving on the best known bound for that problem.

Computational Complexity · Computer Science 2008-10-13 Piotr Berman , Marek Karpinski , Alex Zelikovsky

This paper summarizes the work on implementing few solutions for the Steiner Tree problem which we undertook in the PAAL project. The main focus of the project is the development of generic implementations of approximation algorithms…

Data Structures and Algorithms · Computer Science 2014-10-29 Krzysztof Ciebiera , Piotr Godlewski , Piotr Sankowski , Piotr Wygocki

The prize-collecting Steiner tree problem PCSTP is a well-known generalization of the classical Steiner tree problem in graphs, with a large number of practical applications. It attracted particular interest during the latest (11th) DIMACS…

Optimization and Control · Mathematics 2018-11-26 Daniel Rehfeldt , Thorsten Koch

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

We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, we show how to build a Steiner forest spanner for such graphs.…

Data Structures and Algorithms · Computer Science 2009-11-30 MohammadHossein Bateni , MohammadTaghi Hajiaghayi , Dániel Marx

The Steiner tree problem is a classical NP-hard optimization problem with a wide range of practical applications. In an instance of this problem, we are given an undirected graph G=(V,E), a set of terminals R, and non-negative costs c_e for…

Data Structures and Algorithms · Computer Science 2007-12-24 Jochen Konemann , David Pritchard , Kunlun Tan

The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…

Data Structures and Algorithms · Computer Science 2025-03-07 Stephan Held , Edgar Perner

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Data Structures and Algorithms · Computer Science 2010-06-18 Marek Cygan , Lukasz Kowalik , Marcin Mucha , Marcin Pilipczuk , Piotr Sankowski

In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…

Data Structures and Algorithms · Computer Science 2026-01-06 Radek Hušek , Dušan Knop , Tomáš Masařík

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

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

Our main result is a full classification, for every connected graph $H$, of the computational complexity of Steiner Forest on $H$-subgraph-free graphs. To obtain this dichotomy, we establish the following new algorithmic, hardness, and…

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

We consider Directed Steiner Forest (DSF), a fundamental problem in network design. The input to DSF is a directed edge-weighted graph $G = (V, E)$ and a collection of vertex pairs $\{(s_i, t_i)\}_{i \in [k]}$. The goal is to find a minimum…

Data Structures and Algorithms · Computer Science 2024-10-24 Chandra Chekuri , Rhea Jain

We initiate the study of degree-bounded network design problems in the online setting. The degree-bounded Steiner tree problem { which asks for a subgraph with minimum degree that connects a given set of vertices { is perhaps one of the…

Data Structures and Algorithms · Computer Science 2017-04-19 Sina Dahghani , Soheil Ehsani , MohammadTaghi Hajiaghayi , Vahid Liaghat , Harald Racke

The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…

Data Structures and Algorithms · Computer Science 2024-08-23 Ming Sun , Xinyu Wu , Yi Zhou , Jin-Kao Hao , Zhang-Hua Fu