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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

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

{\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

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

A promising approach for obtaining improved approximation algorithms for Steiner tree is to use the bidirected cut relaxation (BCR). The integrality gap of this relaxation is at least $36/31$, and it has long been conjectured that its true…

Data Structures and Algorithms · Computer Science 2023-09-12 Ali Çivril , Muhammed Mirza Biçer , Berkay Tahsin Tunca , Muhammet Yasin Kangal

We study the prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show…

Data Structures and Algorithms · Computer Science 2016-01-12 Jarosław Byrka , Mateusz Lewandowski , Carsten Moldenhauer

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

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

We give an algorithm that computes a $(1+\epsilon)$-approximate Steiner forest in near-linear time $n \cdot 2^{(1/\epsilon)^{O(ddim^2)} (\log \log n)^2}$. This is a dramatic improvement upon the best previous result due to Chan et al., who…

Computational Geometry · Computer Science 2019-04-09 Lee-Ad Gottlieb , Yair Bartal

Rotation distance between rooted binary trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. We give an efficient,…

Data Structures and Algorithms · Computer Science 2018-03-19 Sean Cleary , Katherine St. John

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 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 rooted Subtree…

Data Structures and Algorithms · Computer Science 2018-11-15 Neil Olver , Frans Schalekamp , Suzanne van der Ster , Leen Stougie , Anke van Zuylen

We present an approximation algorithm for Weighted Tree Augmentation with approximation factor $1+\ln 2 + \varepsilon < 1.7$. This is the first algorithm beating the longstanding factor of $2$, which can be achieved through many standard…

Data Structures and Algorithms · Computer Science 2021-04-16 Vera Traub , Rico Zenklusen

In this paper, we present an exact algorithm for the Steiner tree problem. The algorithm is based on certain pre-computed index structures. Our algorithm offers a practical solution for the Steiner tree problems on graphs of large size and…

Data Structures and Algorithms · Computer Science 2013-05-27 Fang Wei-Kleiner

We give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed eps > 0 and given n terminals in the plane with connection requests between some pairs of terminals, our…

Computational Geometry · Computer Science 2014-02-25 Glencora Borradaile , Philip Klein , Claire Mathieu

Recently Byrka, Grandoni, Rothvoss and Sanita (at STOC 2010) gave a 1.39-approximation for the Steiner tree problem, using a hypergraph-based linear programming relaxation. They also upper-bounded its integrality gap by 1.55. We describe a…

Discrete Mathematics · Computer Science 2010-06-14 Deeparnab Chakrabarty , Jochen Koenemann , David Pritchard

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

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

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 addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…

Data Structures and Algorithms · Computer Science 2019-02-26 Takanori Maehara , Kazutoshi Ando