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 IssueDOI
Critical random graphs and the structure of a minimum spanning tree
TL;DR: In this article, the authors considered the complete graph on n vertices whose edges are weighted by independent and identically distributed edge weights and showed that if the random weights are all distinct, then the expected diameter of such a tree is Θ(n 1-3).
Journal ArticleDOI
Use of the minimum spanning tree model for molecular epidemiological investigation of a nosocomial outbreak of hepatitis C virus infection.
Enea Spada,Luciano Sagliocca,John Sourdis,Anna Rosa Garbuglia,Vincenzo Poggi,Carmela De Fusco,Alfonso Mele +6 more
TL;DR: The MST model, supported by an exhaustive clinical-epidemiological investigation, appears to be a useful tool in tracing the history of transmission in outbreaks of HCV infection.
Journal ArticleDOI
Fast heuristic algorithms for rectilinear steiner trees
TL;DR: An early algorithm by Hanan is shown to have anO(n logn) time implementation using computational geometry techniques, and an extensive review of proposed heuristics is given.
Journal ArticleDOI
Graph Theoretic Analysis of Resting State Functional MR Imaging
TL;DR: The theoretic and practical frontiers of resting state functional MR imaging are highlighted with observations about major avenues for conceptual advances and clinical translation.
Proceedings ArticleDOI
Using certification trails to achieve software fault tolerance
G.F. Sullivan,Gerald M. Masson +1 more
TL;DR: A technique for achieving fault tolerance in hardware and software systems is introduced that uses time and software redundancy for software fault tolerance and can be outlined as follows.
References
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Robert R. Sokal,P.H.A. Sneath +1 more
TL;DR: The authors continued the story of psychology with added research and enhanced content from the most dynamic areas of the field, such as cognition, gender and diversity studies, neuroscience and more, while at the same time using the most effective teaching approaches and learning tools.