Journal ArticleDOI
On the History of the Minimum Spanning Tree Problem
Ron Graham,Pavol Hell +1 more
TLDR
There are several apparently independent sources and algorithmic solutions of the minimum spanning tree problem and their motivations, and they have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century.Abstract:
It is standard practice among authors discussing the minimum spanning tree problem to refer to the work of Kruskal(1956) and Prim (1957) as the sources of the problem and its first efficient solutions, despite the citation by both of Boruvka (1926) as a predecessor. In fact, there are several apparently independent sources and algorithmic solutions of the problem. They have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century. We shall explore and compare these works and their motivations, and relate them to the most recent advances on the minimum spanning tree problem.read more
Citations
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Rapid Restoration Sequence of Fiber Links and Communication Paths from Catastrophic Failures
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A Novel Green Logistics Technique for Planning Merchandise Deliveries: A Case Study
Carlos Hernández-Mejía,Delia Torres-Muñoz,Everardo Inzunza-González,C. Sánchez-López,E. E. García-Guerrero +4 more
TL;DR: In this article , a modified version of the Resistive Grid Path Planning Methodology (RGPPM) is used to establish a path through georeferential locations for delivering merchandise to customers.
Journal ArticleDOI
Solving the Steiner tree problem in graphs by chaotic search
Exact and approximate solving approaches in multi-objective combinatorial optimization, application to the minimum weight spanning tree problem Approches de résolution exacte et approchée en optimisation combinatoire multi-objectif, application au problème de l'arbre couvrant de poids minimal
TL;DR: This thesis deals with several aspects related to solving multi-objective problems, without restriction to the bi-objectives, and proposes a new hybrid approach for the determination of the nondominated set, which is instantiated on the minimum spanning tree problem.
Journal ArticleDOI
New BSP/CGM algorithms for spanning trees:
Jucele Franca de Alencar Vasconcellos,Edson Norberto Cáceres,Henrique Mongelli,Siang Wun Song,Frank Dehne,Jayme Luiz Szwarcfiter +5 more
TL;DR: This article devised new parallel algorithms that do not make use of parallel list ranking procedure and implemented them on graphics processing unit, showing that the BSP/CGM model is suitable for designing general purpose parallel algorithms.
References
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Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
TL;DR: Kurosh and Levitzki as discussed by the authors, on the radical of a general ring and three problems concerning nil rings, Bull Amer Math Soc vol 49 (1943) pp 913-919 10 -, On the structure of algebraic algebras and related rings.
Journal ArticleDOI
Hierarchical clustering schemes
TL;DR: A useful correspondence is developed between any hierarchical system of such clusters, and a particular type of distance measure, that gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data.
Journal ArticleDOI
Shortest connection networks and some generalizations
TL;DR: In this paper, the basic problem of interconnecting a given set of terminals with a shortest possible network of direct links is considered, and a set of simple and practical procedures are given for solving this problem both graphically and computationally.
Book
Principles of numerical taxonomy
Robert R. Sokal,P.H.A. Sneath +1 more
TL;DR: The authors continued the story of psychology with added research and enhanced content from the most dynamic areas of the field, such as cognition, gender and diversity studies, neuroscience and more, while at the same time using the most effective teaching approaches and learning tools.