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
The traveling-salesman problem and minimum spanning trees: Part II
Michael Held,Richard M. Karp +1 more
TL;DR: An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.
Journal ArticleDOI
The application of computers to taxonomy.
TL;DR: A method is described for handling large quantities of taxonomic data by an electronic computer so as to yield the outline of a classification based on equally weighted features that enables Similarity to be expressed numerically, and would allow taxonomic rank to be measured in terms of it.
Journal ArticleDOI
Steiner Minimal Trees
E. N. Gilbert,H. O. Pollak +1 more
TL;DR: A Steiner minimal tree for given points in the plane is a tree which interconnects these points using lines of shortest possible total length as mentioned in this paper, where the length of the shortest possible line is chosen.
Journal ArticleDOI
Matroids and the greedy algorithm
TL;DR: Linear-algebra rank is the solution to an especially tractable optimization problem which are linear programs relative to certain derived polyhedra.