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
More filters
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
More filters
Proceedings ArticleDOI
Computing minimum spanning trees efficiently
Aaron Kershenbaum,R. Van Slyke +1 more
TL;DR: Modifications to both Prim's and Kruskal's Algorithms are introduced which give significant improvements for the complete range of sparseness, and a dramatic reduction in execution time can be obtained for sparse networks when the network under consideration is sparse.
Journal ArticleDOI
A parallel algorithm for constructing minimum spanning trees
TL;DR: A new parallel algorithm is studied that constructs an MST of an N-node graph in time proportional to N lg N, on an N(lg N)-processor computing system.
Journal ArticleDOI
Letter to the Editor---The Maximum Capacity Route Problem
TL;DR: This work considers the problem of finding maximum capacity routes between all pairs of nodes in a network and proposes a solution to this problem that is simple, efficient, and scalable.
Journal ArticleDOI
Formal Procedures for Connecting Terminals with a Minimum Total Wire Length
H. Loberman,A. Weinberger +1 more
TL;DR: Two methods for systematically selecting the shortest connections from a list of possible connections to obtain a minimum total wire length are presented, which will be called a minimum tree.