English
Related papers

Related papers: Vulcan: Solving the Steiner Tree Problem with Grap…

200 papers

We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…

Machine Learning · Computer Science 2018-10-26 Zhuwen Li , Qifeng Chen , Vladlen Koltun

We present a new exact algorithm for the Steiner tree problem in edge-weighted graphs. Our algorithm improves the classical dynamic programming approach by Dreyfus and Wagner. We achieve a significantly better practical performance via…

Data Structures and Algorithms · Computer Science 2015-09-09 Stefan Hougardy , Jannik Silvanus , Jens Vygen

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

The Spanning Tree Congestion (STC) problem is the following NP-hard problem: given a graph $G$, construct a spanning tree $T$ of $G$ minimizing its maximum edge congestion where the congestion of an edge $e\in T$ is the number of edges $uv$…

Data Structures and Algorithms · Computer Science 2026-05-05 Petr Kolman

The problem considered is the following. Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, compute a low-weight spanning tree such that the degree of each vertex is at most its specified…

Data Structures and Algorithms · Computer Science 2015-06-02 S. Fekete , S. Khuller , M. Klemmstein , B. Raghavachari , Neal E. Young

Prize-Collecting Steiner Tree (PCST) is a generalization of the Steiner Tree problem, a fundamental problem in computer science. In the classic Steiner Tree problem, we aim to connect a set of vertices known as terminals using the…

Data Structures and Algorithms · Computer Science 2024-05-08 Ali Ahmadi , Iman Gholami , MohammadTaghi Hajiaghayi , Peyman Jabbarzade , Mohammad Mahdavi

We study the Steiner tree problem on map graphs, which substantially generalize planar graphs as they allow arbitrarily large cliques. We obtain a PTAS for Steiner tree on map graphs, which builds on the result for planar edge weighted…

Data Structures and Algorithms · Computer Science 2019-12-03 Jarosław Byrka , Mateusz Lewandowski , Syed Mohammad Meesum , Joachim Spoerhase , Sumedha Uniyal

Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…

Discrete Mathematics · Computer Science 2024-04-10 Enrique Fita Sanmartín , Christoph Schnörr , Fred A. Hamprecht

We study the Steiner Tree problem on unit disk graphs. Given a $n$ vertex unit disk graph $G$, a subset $R\subseteq V(G)$ of $t$ vertices and a positive integer $k$, the objective is to decide if there exists a tree $T$ in $G$ that spans…

Computational Geometry · Computer Science 2020-04-21 Sujoy Bhore , Paz Carmi , Sudeshna Kolay , Meirav Zehavi

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 Steiner tree problem is a well-known problem in network design, routing, and VLSI design. Given a graph, edge costs, and a set of dedicated vertices (terminals), the Steiner tree problem asks to output a sub-graph that connects all…

Artificial Intelligence · Computer Science 2020-11-10 Johannes K. Fichte , Markus Hecher , Andre Schidler

The Belief Propagation approximation, or cavity method, has been recently applied to several combinatorial optimization problems in its zero-temperature implementation, the max-sum algorithm. In particular, recent developments to solve the…

Data Structures and Algorithms · Computer Science 2019-01-04 Alfredo Braunstein , Anna Paola Muntoni

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

Finding the minimum spanning tree (MST) of a graph is an important task in computer vision, as it enables a sparse and low-cost representation of connectivity among elements (such as superpixels, points, or regions), which is useful for…

In the last few years, graph convolutional networks (GCN) have become a popular research direction in the machine learning community to tackle NP-hard combinatorial optimization problems (COPs) defined on graphs. While the obtained results…

Machine Learning · Computer Science 2021-06-02 Elisabeth Gaar , Markus Sinnl

Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by…

Machine Learning · Computer Science 2022-01-26 Maximilian Böther , Otto Kißig , Martin Taraz , Sarel Cohen , Karen Seidel , Tobias Friedrich

The Steiner tree problem is one of the classic and most fundamental $\mathcal{NP}$-hard problems: given an arbitrary weighted graph, seek a minimum-cost tree spanning a given subset of the vertices (terminals). Byrka \emph{et al}. proposed…

Data Structures and Algorithms · Computer Science 2018-11-02 Chi-Yeh Chen

Planning for sequential robotics tasks often requires integrated symbolic and geometric reasoning. TAMP algorithms typically solve these problems by performing a tree search over high-level task sequences while checking for kinematic and…

In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…

Computational Geometry · Computer Science 2021-04-12 Sanjana Dey , Ramesh K. Jallu , Subhas C. Nandy

Software-Defined Networking (SDN) enables flexible network resource allocations for traffic engineering, but at the same time the scalability problem becomes more serious since traffic is more difficult to be aggregated. Those crucial…

Networking and Internet Architecture · Computer Science 2014-05-09 Liang-Hao Huang , Hui-Ju Hung , Chih-Chung Lin , De-Nian Yang