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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Posted ContentDOI
Combining complex networks and data mining: why and how
Massimiliano Zanin,David Papo,Pedro Sousa,Ernestina Menasalvas,Andrea Nicchi,Elaine Kubik,Stefano Boccaletti +6 more
TL;DR: The starting point of this review is that these two fields can in fact advantageously be used in a synergistic manner, and that this state of affairs should be put down to contingent rather than conceptual differences.
Book ChapterDOI
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
TL;DR: This work presents a deterministic algorithm for computing the sensitivity of a minimum spanning tree or shortest path tree in O(m log α(m,n) time, where α is the inverse-Ackermann function.
Journal ArticleDOI
Quantifying loss of information in network-based dimensionality reduction techniques
TL;DR: In this article, the authors developed a framework based on algorithmic information theory to quantify the extent to which information is preserved when network motif analysis, graph spectra and spectral sparsification methods are applied to over twenty different biological and artificial networks.
Journal ArticleDOI
Improvements to the relational fuzzy c-means clustering algorithm
TL;DR: This article compares five methods for Euclideanizing D to D and concludes that the subdominant ultrametric transformation is a clear winner, producing much better partitions of D ˜ than the other four methods.
Journal ArticleDOI
Measuring urban forms from inter-building distances: combining MST graphs with a local index of spatial association
TL;DR: A new method is proposed for characterising local urban patterns at the scale of a large urban region that overcomes the difficulties of surface-based representations of built-up morphologies and provides an efficient way to account for the proximity of built and non-built land.
References
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Journal ArticleDOI
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Book
Principles of numerical taxonomy
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.