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
An Algorithm for Finding K Minimum Spanning Trees
TL;DR: This paper presents an algorithm for finding K minimum spanning trees in an undirected graph based on three subroutines which obtains the kth minimum spanning tree in $O(m)$ steps when the jthminimum spanning trees for $j = 1,2, \cdots ,k - 1$ are given.
Journal ArticleDOI
Improvements of the Held-Karp algorithm for the symmetric traveling-salesman problem.
Keld Helbig Hansen,Jakob Krarup +1 more
TL;DR: A highly efficient algorithm (HK) devised by Held and Karp for solving the symmetric traveling-salesman problem was presented at the 7th Mathematical programming Symposium in 1970 and published in Mathematical Programming in 1971.
Journal ArticleDOI
The Design or Multipoint Linkages in a Teleprocessing Tree Network
K. M. Chandy,Robert A. Russell +1 more
TL;DR: It is shown experimentally that Martin's and Esau-Williams heuristics are, in fact, near-optimal heurstics in the sense that the solutions provided by these heuristic are generally very near the optimal solution.