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We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which…

Computational Complexity · Computer Science 2019-11-22 Lehilton Lelis Chaves Pedrosa , Hugo Kooki Kasuya Rosado

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

This paper studies a 4-approximation algorithm for k-prize collecting Steiner tree problems. This problem generalizes both k-minimum spanning tree problems and prize collecting Steiner tree problems. Our proposed algorithm employs two…

Computational Complexity · Computer Science 2018-02-20 Yusa Matsuda , Satoshi Takahashi

The \emph{Steiner tree} problem is one of the fundamental and classical problems in combinatorial optimization. In this paper, we study this problem in the $\mathcal{CONGESTED}$ $\mathcal{CLIQUE}$ model of distributed computing and present…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-31 Parikshit Saikia , Sushanta Karmakar

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

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

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

We present four novel approximation algorithms for finding triangulation of minimum treewidth. Two of the algorithms improve on the running times of algorithms by Robertson and Seymour, and Becker and Geiger that approximate the optimum by…

Data Structures and Algorithms · Computer Science 2013-01-14 Eyal Amir

In the Steiner Forest problem, we are given a graph and a collection of source-sink pairs, and the goal is to find a subgraph of minimum total length such that all pairs are connected. The problem is APX-Hard and can be 2-approximated by,…

Data Structures and Algorithms · Computer Science 2017-07-11 Martin Groß , Anupam Gupta , Amit Kumar , Jannik Matuschke , Daniel R. Schmidt , Melanie Schmidt , José Verschae

There is a large discrepancy in our understanding of uncapacitated and capacitated versions of network location problems. This is perhaps best illustrated by the classical k-center problem: there is a simple tight 2-approximation algorithm…

Data Structures and Algorithms · Computer Science 2013-04-11 Hyung-Chan An , Aditya Bhaskara , Ola Svensson

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 design a 3/2 approximation algorithm for the Generalized Steiner Tree problem (GST) in metrics with distances 1 and 2. This is the first polynomial time approximation algorithm for a wide class of non-geometric metric GST instances with…

Computational Complexity · Computer Science 2008-12-12 Piotr Berman , Marek Karpinski , Alex Zelikovsky

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

Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$)…

Computational Geometry · Computer Science 2015-04-13 Stephan Held , Nicolas Kämmerling

Uniform cost-distance Steiner trees minimize the sum of the total length and weighted path lengths from a dedicated root to the other terminals. They are applied when the tree is intended for signal transmission, e.g. in chip design or…

Data Structures and Algorithms · Computer Science 2025-07-31 Josefine Foos , Stephan Held , Yannik Kyle Dustin Spitzley

The classical algorithm of Agrawal, Klein and Ravi [SIAM J. Comput., 24 (1995), pp. 440-456], stated in the setting of the primal-dual schema by Goemans and Williamson [SIAM J. Comput., 24 (1995), pp. 296-317] uses the undirected cut…

Data Structures and Algorithms · Computer Science 2019-11-19 Ali Çivril

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

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

Data Structures and Algorithms · Computer Science 2026-04-29 Michał Szyfelbein

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated…

Numerical Analysis · Mathematics 2018-07-17 Fabio Nobile , Raul Tempone , Soeren Wolfers

Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…

Optimization and Control · Mathematics 2025-06-24 Du-Yi Wang , Guo Liang , Guangwu Liu , Kun Zhang