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Related papers: Statistical Mechanics of Steiner trees

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We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…

Data Structures and Algorithms · Computer Science 2025-04-24 Jiwei Zhang , Deepak Ajwani

Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is…

Data Structures and Algorithms · Computer Science 2015-08-07 Rico Zenklusen

We study the problem of privately releasing an approximate minimum spanning tree (MST). Given a graph $G = (V, E, \vec{W})$ where $V$ is a set of $n$ vertices, $E$ is a set of $m$ undirected edges, and $ \vec{W} \in \mathbb{R}^{|E|} $ is an…

Data Structures and Algorithms · Computer Science 2024-12-16 Rasmus Pagh , Lukas Retschmeier , Hao Wu , Hanwen Zhang

This paper presents a randomized Las Vegas distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-25 Gopal Pandurangan , Peter Robinson , Michele Scquizzato

We study the minimum spanning tree (MST) problem in the massively parallel computation (MPC) model. Our focus is particularly on the *strictly sublinear* regime of MPC where the space per machine is $O(n^\delta)$. Here $n$ is the number of…

Data Structures and Algorithms · Computer Science 2025-10-10 Amir Azarmehr , Soheil Behnezhad , Rajesh Jayaram , Jakub Łącki , Vahab Mirrokni , Peilin Zhong

The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree $T$ for graph $G=(V,E)$ with $n$ vertices, such that the maximum degree $d$ of $T$ is the smallest among all spanning trees of $G$. In this paper,…

Data Structures and Algorithms · Computer Science 2018-06-12 Michael Dinitz , Magnús M. Halldórsson , Calvin Newport

Network design under uncertainty arises in countless real-world settings and can be captured by the Stochastic Steiner Tree Problem (SSTP). Although there are a few approaches specifically tailored to this stochastic optimization problem,…

Optimization and Control · Mathematics 2026-03-02 Berend Markhorst , Alessandro Zocca , Joost Berkhout , Rob van der Mei

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

Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…

Data Structures and Algorithms · Computer Science 2025-05-13 Xiangyun Ding , Yan Gu , Yihan Sun

Choi et. al (2011) introduced a minimum spanning tree (MST)-based method called CLGrouping, for constructing tree-structured probabilistic graphical models, a statistical framework that is commonly used for inferring phylogenetic trees.…

Combinatorics · Mathematics 2017-01-12 Prabhav Kalaghatgi , Thomas Lengauer

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Due to this geometric universality, we are able to characterise the energy of MST using a scaling distribution ($P(\epsilon)$) found using uniform…

Statistical Mechanics · Physics 2009-11-07 R. Dobrin , P. M. Duxbury

We consider two natural variants of the problem of minimum spanning tree (MST) of a graph in the parallel setting: MST verification (verifying if a given tree is an MST) and the sensitivity analysis of an MST (finding the lowest cost…

Data Structures and Algorithms · Computer Science 2024-08-02 Sam Coy , Artur Czumaj , Gopinath Mishra , Anish Mukherjee

Given a graph $G = (V,E)$ and a subset $T \subseteq V$ of terminals, a \emph{Steiner tree} of $G$ is a tree that spans $T$. In the vertex-weighted Steiner tree (VST) problem, each vertex is assigned a non-negative weight, and the goal is to…

Data Structures and Algorithms · Computer Science 2019-05-07 Faryad Darabi Sahneh , Alon Efrat , Stephen Kobourov , Spencer Krieger , Richard Spence

Modern approaches to the search of Relative and Global minima of potential energy function of Biomacromolecular structures include techniques of combinatorial optimization like the study of Steiner Points and Steiner Trees. These methods…

Mathematical Physics · Physics 2007-05-23 R. P. Mondaini

Steiner Tree Problem (STP) in graphs aims to find a tree of minimum weight in the graph that connects a given set of vertices. It is a classic NP-hard combinatorial optimization problem and has many real-world applications (e.g., VLSI chip…

Machine Learning · Computer Science 2021-11-23 Haizhou Du , Zong Yan , Qiao Xiang , Qinqing Zhan

The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…

Data Structures and Algorithms · Computer Science 2024-08-23 Ming Sun , Xinyu Wu , Yi Zhou , Jin-Kao Hao , Zhang-Hua Fu

The Steiner Tree Problem (STP) in graphs is an important problem with various applications in many areas such as design of integrated circuits, evolution theory, networking, etc. In this paper, we propose an algorithm to solve the STP. The…

Artificial Intelligence · Computer Science 2018-06-19 Matthieu De Laere , San Tu Pham , Patrick De Causmaecker

In the area of evolutionary computation the calculation of diverse sets of high-quality solutions to a given optimization problem has gained momentum in recent years under the term evolutionary diversity optimization. Theoretical insights…

Neural and Evolutionary Computing · Computer Science 2021-04-28 Jakob Bossek , Frank Neumann

This paper addresses combinatorial optimization scheme for solving the multicriteria Steiner tree problem for communication network topology design (e.g., wireless mesh network). The solving scheme is based on several models: multicriteria…

Data Structures and Algorithms · Computer Science 2011-02-15 Mark Sh. Levin , Rustem I. Nuriakhmetov

Minimal spanning trees (MSTs) have been used in cosmology and astronomy to distinguish distributions of points in a multi-dimensional space. They are essentially unknown in particle physics, however. We briefly define MSTs and illustrate…

Applications · Statistics 2017-03-08 Jessica Lovelace Rainbolt , Michael Schmitt