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
Transportation Routing Map Abstraction Approach: Algorithm and Numerical Analysis
Lei Zhu,Yi-Chang Chiu +1 more
TL;DR: The outcome of the proposed algorithm is an abstract map that retains the original detailed map's hierarchical structure with high topological connectivity quality at a significant computation saving.
Journal ArticleDOI
Finding Outbreak Trees in Networks with Limited Information
TL;DR: This paper addresses the problem of identifying contagion patterns responsible for the spread of a disease in a network, which can be applied in real-time to evaluate an ongoing outbreak and proposes a novel formulation and solution method based on a two-step heuristic.
A socio-technical perspective on requirements engineering
TL;DR: In this paper, the authors propose a novel approach to solve the problem of unstructured data in the context of data augmentation, which is based on the concept of "data augmentation".
Journal ArticleDOI
Source clustering in the Hi-GAL survey determined using a minimum spanning tree method
M. Beuret,Nicolas Billot,L. Cambrésy,David Eden,Davide Elia,Sergio Molinari,Stefano Pezzuto,Eugenio Schisano +7 more
TL;DR: In this article, the authors investigated the clustering of the far-infrared sources from the Herschel infrared Galactic Plane Survey (Hi-GAL) in the Galactic longitude range of 71 to 67 deg.
Journal ArticleDOI
Minimum bottleneck spanning trees with degree bounds
Patrick J. Andersen,Charl J. Ras +1 more
TL;DR: The δ‐MBST problem, which is the problem of finding an MBST such that every vertex in the tree has degree at most δ, is introduced, and it is established that theδ‐ MBST problem is NP‐complete for any δ ≥ 2 and NP‐hard for δ = 2 and 3, and tractable forδ ≥ 5.
References
More filters
Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
TL;DR: Kurosh and Levitzki as discussed by the authors, on the radical of a general ring and three problems concerning nil rings, Bull Amer Math Soc vol 49 (1943) pp 913-919 10 -, On the structure of algebraic algebras and related rings.
Journal ArticleDOI
Hierarchical clustering schemes
TL;DR: A useful correspondence is developed between any hierarchical system of such clusters, and a particular type of distance measure, that gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data.
Journal ArticleDOI
Shortest connection networks and some generalizations
TL;DR: In this paper, the basic problem of interconnecting a given set of terminals with a shortest possible network of direct links is considered, and a set of simple and practical procedures are given for solving this problem both graphically and computationally.
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.