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Related papers: Minimum spanning trees on random networks

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Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…

Machine Learning · Statistics 2025-10-16 Marek Gagolewski , Anna Cena , Maciej Bartoszuk , Łukasz Brzozowski

Consider~\(n\) nodes distributed independently across~\(N\) cities contained with the unit square~\(S\) according to a distribution~\(f.\) Each city is modelled as an~\(r_n \times r_n\) square contained within~\(S\) and~\(MSTC_n\) denotes…

Probability · Mathematics 2018-01-10 Ghurumuruhan Ganesan

In this paper, we study the form over the minimum spanning tree problem (MST) from which we will derive an intuitively generalized model and new methods with the upper bound of runtimes of logarithm. The new pattern we made has taken…

Discrete Mathematics · Computer Science 2017-06-26 Yong Tan

In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…

Distributed, Parallel, and Cluster Computing · Computer Science 2007-05-23 Pradosh Kumar Mohapatra

Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributed in the unit square~\(S,\) each according to a distribution~\(f\) and let~\(K_n\) be the complete graph formed by joining each pair of nodes by a straight line…

Probability · Mathematics 2023-05-15 Ghurumuruhan Ganesan

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

The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant,…

Combinatorics · Mathematics 2024-05-31 Nikita Zvonkov

With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…

Combinatorics · Mathematics 2017-12-12 Lan Lin , Yixun Lin

A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…

Probability · Mathematics 2012-06-19 Michael Aizenman , Almut Burchard , Charles M. Newman , David B. Wilson

We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose…

Probability · Mathematics 2022-05-11 Louigi Addario-Berry , Jordan Barrett , Benoît Corsini

In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative $(1+\delta)$ of uniform in expected…

Data Structures and Algorithms · Computer Science 2009-08-12 Jonathan A. Kelner , Aleksander Madry

For any edge weight distribution, we consider the uniform spanning tree (UST) on finite graphs with i.i.d. random edge weights. We show that, for bounded degree expander graphs and finite boxes of ${\mathbb Z}^d$, the diameter of the UST is…

Probability · Mathematics 2024-10-23 Luca Makowiec , Michele Salvi , Rongfeng Sun

We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-12-12 Franck Butelle , Christian Lavault , Marc Bui

Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…

Metric Geometry · Mathematics 2014-03-18 A. O. Ivanov , A. A. Tuzhilin

Transport in weighted networks is dominated by the minimum spanning tree (MST), the tree connecting all nodes with the minimum total weight. We find that the MST can be partitioned into two distinct components, having significantly…

Disordered Systems and Neural Networks · Physics 2009-11-11 Zhenhua Wu , Lidia A. Braunstein , Shlomo Havlin , H. Eugene Stanley

We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…

Disordered Systems and Neural Networks · Physics 2015-06-25 Tomer Kalisky , Sameet Sreenivasan , Lidia A. Braunstein , Sergey V. Buldyrev , Shlomo Havlin , H. Eugene Stanley

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle…

Data Structures and Algorithms · Computer Science 2016-11-25 Lélia Blin , Maria Gradinariu Potop-Butucaru , Stephane Rovedakis , Sébastien Tixeuil

We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…

Probability · Mathematics 2024-01-26 Gourab Ray , Arnab Sen

We study smoothed analysis of distributed graph algorithms, focusing on the fundamental minimum spanning tree (MST) problem. With the goal of studying the time complexity of distributed MST as a function of the "perturbation" of the input…

Data Structures and Algorithms · Computer Science 2019-11-11 Soumyottam Chatterjee , Gopal Pandurangan , Nguyen Dinh Pham

Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…

Data Structures and Algorithms · Computer Science 2010-05-24 Viswanath Gunturi , Shashi Shekhar , Arnab Bhattacharya