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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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Weight-Constrained Minimum Spanning Tree Problem

TL;DR: In this article, a literature overview on minimum spanning tree problem, theoretical properties concerning the convex hull and the Lagrangian relaxation are given, and some in-and exclusion-test for this problem is presented.
Journal ArticleDOI

Contact Plan Design for GNSS Constellations: A Case Study With Optical Intersatellite Links

TL;DR: In this article , the authors present a contact plan design scheme based on a degree constrained minimum spanning tree heuristic applied to such OISL-enabled Global Navigation Satellite System (O-GNSS) constellations.
Journal ArticleDOI

Feature-based groupwise registration of historical aerial images to present-day ortho-photo maps

TL;DR: The superiority of the proposed method over existing pairwise and groupwise registration methods is demonstrated on eight highly challenging sets of historical images with corresponding ortho-photo maps.
Book ChapterDOI

How to Find a Minimum Spanning Tree in Practice

TL;DR: The factors that influence the actual running time of an algorithm are reviewed, from choice of language, machine, and compiler, through low-level implementation choices, to purely algorithmic issues.
BookDOI

Applications of Discrete Geometry and Mathematical Morphology

TL;DR: This paper gives an overview of the most important algorithms for contour reconstruction and shows that a relatively new algorithm, called ‘cleaned refinement reduction’ is the most robust one with regard to significant background noise and even shows a reconstruction ability being similar to the one of a child at the age of 4.
References
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Journal ArticleDOI

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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.