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
More filters
Dissertation
Automated Selection of Modelling Coordinates for Forward Dynamic Analysis of Multibody Systems
TL;DR: Two tree selection algorithms capable of estimating the tree set, and hence coordinate set, that produces models having the fastest forward dynamic simulation times are developed.
Proceedings ArticleDOI
A Study Framework of Industrial Electricity-Consumption Correlation Clustering: Taking Xiaoshan Textile Industry as Example
TL;DR: Based on daily industrial electricity-consumption data, a study framework of industry clustering is proposed in this paper, which consists of qualitative analysis, clustering and forecast, and it is found that industries in the same category show strong similarity in electricity consumption pattern, on the basis of which a clustering analysis is made with Pearson-correlation-coefficient-based distance and Minimum Spanning Tree method.
Proceedings ArticleDOI
Keyphrase-Based Hierarchical Clustering for Arabic Documents
TL;DR: A domain independent approach, which builds a hierarchical meaningful clustering tree that overcomes the problem of high dimensionality of feature vector by representing each document with its keyphrases, and introduced a new similarity measure by taking the common lemma form keyphRases among feature vectors of documents.
Book ChapterDOI
On morphological hierarchical representations for image processing and spatial data clustering
Pierre Soille,Laurent Najman +1 more
TL;DR: In this article, a survey of hierarchical clustering in the context of mathematical morphology is presented, with a focus on constrained connectivity and ultrametric watersheds, two paradigms developed for the hierarchical representation of images.
References
More filters
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.