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
Steiner trees, steiner circuits and the interference problem in building design
TL;DR: In this paper, the authors describe heuristic algorithms for the interactive development of minimal Steiner trees and circuits, which enables architects and engineers to design these systems in ways consistent with the designed arrangement of building activities in two and three dimensions.
Journal ArticleDOI
The Shortest Hamiltonian Chain of a Graph
TL;DR: Two basic algorithms are given each of which can solve both of the above problems with only slight modification, and whereas the convergence of Algorithm A is self-evident, no proof of convergence has been obtained for Algorithm B.
Journal ArticleDOI
Survey of Deterministic Networks
TL;DR: The state-of-the-art of deterministic networks is surveyed with a discussion of shortest path, transportation, assignment, transshipment, maximum flow, minimum spanning tree, Chinese postman, Euler path and multicommodity flow models.