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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Proceedings ArticleDOI
Analysis of similarities between stock and cryptocurrency series by using graphs and spanning trees
Mariana Durcheva,Pavel Tsankov +1 more
TL;DR: The results show that cryptocurrencies and companies with high capitalization tend to correspond to central and densely connected nodes, unlike the graphs of NASDAQ stocks, where clusters of nodes having small dissimilarities are observed.
Journal ArticleDOI
Integer Programming Formulations for Minimum Spanning Tree Interdiction
TL;DR: This paper studies an alternative integer program derived directly from the attacker’s solution space and shows that this formulation yields a stronger linear relaxation than the bilevel counterpart, and presents several technical developments, including a detailed study of the problem's solution space, multiple formulations, and a polyhedral analysis of the convex hull of feasible solutions.
Book ChapterDOI
Clustering Techniques and their Applications
TL;DR: This article will overview recent research work which appears to be very promising, and will also pinpoint difficult issues arising, and indicate the latent potential for further gains in clustering.
Journal ArticleDOI
THE MINIMUM SPANNING TREE PROBLEM: Jarník's solution in historical and present context
TL;DR: Algorithms solving several other graph problems, based of Jarnik's approach to the solution of the MST problem, are discussed in conjunction with the properties of the Breadth-First-Search Tree and Depth- first- search Tree.
Journal ArticleDOI
IBRIDIA: A hybrid solution for processing big logistics data
TL;DR: This paper presents a hybrid framework for processing massive volume of data in batch style and real-time, built upon Johnson’s hierarchical clustering (HCL) algorithm which produces a dendrogram that represents different clusters of data objects.
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.