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Journal ArticleDOI

On the History of the Minimum Spanning Tree Problem

Ron Graham, +1 more
- 01 Jan 1985 - 
- Vol. 7, Iss: 1, pp 43-57
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.

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Citations
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Journal ArticleDOI

Identifying Different Meanings of a Chinese Morpheme through Semantic Pattern Matching in Augmented Minimum Spanning Trees

TL;DR: This work theoretically defined and detailed what are the Chinese semantic patterns to be searched in the augmented minimum spanning trees and modified the computational approach to include the use of Nearest Neighbors lists, allowing for a major contribution.
Proceedings ArticleDOI

Optimal Relay Node Placement for Connectivity Recovery in Underwater Acoustic Sensor Networks

TL;DR: This work studied the crucial issue to reestablish the network connectivity with the least number of relay nodes which is NP-hard in general and proposes a novel heuristic scheme for UASNs which works based on a 3 dimensional architecture.
Posted Content

The Atlas for the Aspiring Network Scientist

TL;DR: In this paper, the authors present an "Atlas" of the field of network science, which is the field dedicated to the investigation and analysis of complex systems via their representations as networks.
Book ChapterDOI

The minimum-area spanning tree problem

TL;DR: It is proved that the Euclidean minimum spanning tree of $\mathcal{P}$ is a constant-factor approximation for mast, and this result is applied to obtain constant-Factor approximations for the Minimum-Area Range Assignment (mara) problem, for the minimum-Area Connected Disk Graph (macdg)problem, and for theminimum-Area Tour (mat) problem.
Proceedings ArticleDOI

The generalized approaches of genetic algorithms on constrained minimum spanning tree problems

TL;DR: It is emphasized that it is possible for GAs to generalize the problem-solving as long as the problems at hand can be generalized in data structure of solutions.
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

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.