English
Related papers

Related papers: Steiner Forest: A Simplified Better-Than-2 Approxi…

200 papers

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

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

This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…

Data Structures and Algorithms · Computer Science 2021-11-22 Étienne Bamas , Marina Drygala , Andreas Maggiori

We achieve a (randomized) polynomial-time approximation scheme (PTAS) for the Steiner Forest Problem in doubling metrics. Before our work, a PTAS is given only for the Euclidean plane in [FOCS 2008: Borradaile, Klein and Mathieu]. Our PTAS…

Data Structures and Algorithms · Computer Science 2016-08-24 T-H. Hubert Chan , Shuguang Hu , Shaofeng H. -C. Jiang

Given an edge-weighted graph and a set of known seed vertices, a network scientist often desires to understand the graph relationships to explain connections between the seed vertices. When the seed set is 3 or larger Steiner minimal tree -…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-31 Tahsin Reza , Geoffrey Sanders , Roger Pearce

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

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 Forest Augmentation Problem (FAP) asks for a minimum set of additional edges (links) that make a given forest 2-edge-connected while spanning all vertices. A key special case is the Path Augmentation Problem (PAP), where the input…

Data Structures and Algorithms · Computer Science 2025-05-22 Felix Hommelsheim

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the Subtree…

Data Structures and Algorithms · Computer Science 2016-04-29 Frans Schalekamp , Anke van Zuylen , Suzanne van der Ster

The best algorithm for approximating Steiner tree has performance ratio $\ln(4)+\epsilon \approx 1.386$ [J. Byrka et al., \textit{Proceedings of the 42th Annual ACM Symposium on Theory of Computing (STOC)}, 2010, pp. 583-592], whereas the…

Computational Complexity · Computer Science 2017-02-21 Ali Çivril

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error e from 120 degrees.This notion arises in numerical approximations of…

Metric Geometry · Mathematics 2020-02-25 Charl Ras , Konrad J. Swanepoel , Doreen Thomas

It was recently found that there are very close connections between the existence of additive spanners (subgraphs where all distances are preserved up to an additive stretch), distance preservers (subgraphs in which demand pairs have their…

Data Structures and Algorithms · Computer Science 2016-07-21 Eden Chlamtáč , Michael Dinitz , Guy Kortsarz , Bundit Laekhanukit

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

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

Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the…

Data Structures and Algorithms · Computer Science 2013-04-30 MohammadHossein Bateni , MohammadTaghi Hajiaghayi , Vahid Liaghat

{\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 basic goal of survivable network design is to build cheap networks that guarantee the connectivity of certain pairs of nodes despite the failure of a few edges or nodes. A celebrated result by Jain [Combinatorica'01] provides a…

Data Structures and Algorithms · Computer Science 2022-04-21 Fabrizio Grandoni , Afrouz Jabal Ameli , Vera Traub

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

In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The…

Data Structures and Algorithms · Computer Science 2022-11-15 R. Ravi , Weizhong Zhang , Michael Zlatin

We propose a simple and natural approximation algorithm for the problem of finding a 2-edge-connected spanning subgraph of minimum total edge cost in a graph. The algorithm maintains a spanning forest starting with an empty edge set. In…

Data Structures and Algorithms · Computer Science 2018-11-21 Stephan Beyer , Markus Chimani , Joachim Spoerhase