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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Journal ArticleDOI
Fibonacci heaps and their uses in improved network optimization algorithms
TL;DR: Using F-heaps, a new data structure for implementing heaps that extends the binomial queues proposed by Vuillemin and studied further by Brown, the improved bound for minimum spanning trees is the most striking.
Proceedings ArticleDOI
Fibonacci Heaps And Their Uses In Improved Network Optimization Algorithms
TL;DR: The structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown to obtain improved running times for several network optimization algorithms.
Journal ArticleDOI
Algorithms for hierarchical clustering: an overview
TL;DR: A recently developed very efficient (linear time) hierarchical clustering algorithm is described, which can also be viewed as a hierarchical grid‐based algorithm.
Book
Handbook of Combinatorial Optimization
Ding-Zhu Du,Panos M. Pardalos +1 more
TL;DR: The Steiner Ratio of Banach-Minkowski Space and Probabilistic Verification and Non-Approximability and Network-Based Model and Algorithms in Data Mining and Knowledge Discovery are studied.
References
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Journal ArticleDOI
Elementary Linkage Analysis for Isolating Orthogonal and Oblique Types and Typal Relevancies
Journal ArticleDOI
Applications of Path Compression on Balanced Trees
TL;DR: A method for computing functions defined on paths in trees based on tree manipulation techniques first used for efficiently representing equivalence relations, which has an almost-linear running time and is useful for solving certain kinds of pathfinding problems on reducible graphs.
Journal ArticleDOI
Sur la liaison et la division des points d'un ensemble fini
Journal ArticleDOI
On teleprocessing system design: part II a method for approximating the optimal network
L. R. Esau,K. C. Williams +1 more
TL;DR: An iterative method for obtaining an approximation solution to an optimum network is presented and it is assumed that an acceptable line utilization factor is given.
Journal ArticleDOI
Set Merging Algorithms
TL;DR: This paper considers the problem of merging sets formed from a total of n items in such a way that at any time, the name of a set containing a given item can be ascertained.