English
Related papers

Related papers: Reduction-based exact solution of prize-collecting…

200 papers

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

We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…

Data Structures and Algorithms · Computer Science 2023-04-13 Jannis Blauth , Martin Nägele

The Steiner tree problems are well-known NP-hard problems that have diverse applications. Duin et al. (2004) have intuitively proposed the widely-used transformation from the classical group Steiner tree problem to the classical Steiner…

Discrete Mathematics · Computer Science 2019-04-09 Yahui Sun

Graph packing problem is one of the central problems in graph theory and combinatorial optimization. The famous Steiner tree packing problem in undirected graphs has become an well-established area. It is natural to extend this problem to…

Combinatorics · Mathematics 2026-05-19 Yuefang Sun

Minimum Spanning Trees are a well-studied subset of graph problems. While classical algorithms have existed to solve these problems for decades, new variations and application areas are constantly being discovered. When dealing with large…

Data Structures and Algorithms · Computer Science 2023-12-29 Arjun Bhalla

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 consider a multistage framework introduced recently where, given a time horizon t=1,2,...,T, the input is a sequence of instances of a (static) combinatorial optimization problem I_1,I_2,...,I_T, (one for each time step), and the goal is…

Data Structures and Algorithms · Computer Science 2019-09-24 Evripidis Bampis , Bruno Escoffier , Alexander Kononov

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 study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good…

Data Structures and Algorithms · Computer Science 2016-06-27 Jakub Łącki , Jakub Oćwieja , Marcin Pilipczuk , Piotr Sankowski , Anna Zych

In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in metric spaces, a generalization of the well-known Steiner tree problem. Cost-distance Steiner trees minimize the sum of the total length and the weighted path…

Data Structures and Algorithms · Computer Science 2022-11-10 Stephan Held , Yannik Kyle Dustin Spitzley

A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…

Quantum Physics · Physics 2020-07-16 Masayuki Miyamoto , Masakazu Iwamura , Koichi Kise , François Le Gall

Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…

Machine Learning · Computer Science 2023-05-02 Reyan Ahmed , Mithun Ghosh , Kwang-Sung Jun , Stephen Kobourov

In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-13 Lélia Blin , Maria Gradinariu Potop-Butucaru , Stephane Rovedakis

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

The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…

Computational Complexity · Computer Science 2025-12-08 Arash Beikmohammadi , Andrei A. Bulatov

The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity…

Statistical Mechanics · Physics 2009-11-13 M. Bayati , C. Borgs , A. Braunstein , J. Chayes , A. Ramezanpour , R. Zecchina

In this paper, we study the prize-collecting rural postman problem (PCRPP), a variant of the rural postman problem. Given a PCRPP instance consisting of an undirected graph whose edges have nonnegative lengths and nonnegative profits,…

Data Structures and Algorithms · Computer Science 2026-05-26 Hong Li , Jianping Li , Wei Li , Runtao Xie , Xiaoxiao Yang

We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our…

Combinatorics · Mathematics 2020-02-11 Matias Siebert , Shabbir Ahmed , George Nemhauser

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

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