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
Iraqi stock market structure analysis based on minimum spanning tree
TL;DR: In this article , the authors described the network model of the stock market as a complete weighted graph and investigated the Iraqi stock markets using graph theory tools, where the vertices of this graph correspond to the Iraqi markets companies, and the weights of the edges are set ulrametric distance of minimum spanning tree.
Journal ArticleDOI
Greedy Families for Linear Objective Functions
TL;DR: In this article, the authors characterized families of feasible subsets of a finite set for which the greedy algorithm returns the optimum subset independent of the weighting of a linear objective function on the set.
Proceedings ArticleDOI
Seed Extension Based Interactive Medical Volume Segmentation Method
TL;DR: The proposed interactive segmentation method performs 10 times faster when segmenting volumes composed of more than 240 slices, as the time complexity of constructing MSF is quasi-linear, whereas the min-cut/max-flow is polynomial.
Posted Content
On Minimum Spanning Trees for Random Euclidean Bipartite Graphs
Mario Correddu,Dario Trevisan +1 more
TL;DR: In this article, the authors considered the minimum spanning tree problem on a weighted complete bipartite graph and showed that the maximum vertex degree of the tree grows logarithmically, in contrast with the classical, non-bipartite, case, where a uniform bound holds depending on $d$ only.
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.