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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Percolation on complex networks: Theory and application
TL;DR: The percolation theory has already percolated into the researches of structure analysis and dynamic modeling in network science, such as robustness, epidemic spreading, vital node identification, and community detection.
Posted Content
On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems
TL;DR: The classical Bird tree allocation of minimum cost spanning tree problems is obtained as a particular case in the algorithm for the irreducible core and the paper characterizes these solutions axiomatically.
Journal ArticleDOI
The problem of the optimal biobjective spanning tree
TL;DR: The solution to the problem of finding the set of optimal spanning trees of a connected graph is described through an algorithm that builds the family of efficient trees, considering two cost functions defined on theSet of edges.
Journal ArticleDOI
Low-degree minimum spanning trees
Gabriel Robins,Jeffrey S. Salowe +1 more
TL;DR: It is proved that, under theLp norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball, and an even tighter bound for M STs where the maximum degree is minimized is shown.
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Protein Pockets: Inventory, Shape, and Comparison
Ryan G. Coleman,Kim A. Sharp +1 more
TL;DR: This method is called CLIPPERS for complete liberal inventory of protein pockets elucidating and reporting on shape, which guarantees that any pocket of interest will be found among the output pockets, unlike all previous methods of pocket identification.
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.