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
Upper and lower bounding strategies for the generalized minimum spanning tree problem
TL;DR: The generalized minimum spanning tree problem (GMST), which requires spanning at least one vertex out of every set of disjoint vertices in a graph, is addressed, it is shown that the geometric version of this problem is NP -hard, and two stochastic heuristics are proposed.
Journal ArticleDOI
Algorithms to solve the knapsack constrained maximum spanning tree problem
TL;DR: This work proves the knapsack problem 𝒩𝒫-hard, presents upper and lower bounds, develops a branch-and-bound algorithm to solve the problem to optimality and proposes a shooting method to accelerate computation.
Journal ArticleDOI
Information Visualization for DNA Microarray Data Analysis: A Critical Review
TL;DR: This paper explains how graphical representation can be applied in general to this problem domain, followed by exploring the role of visualization in gene expression data analysis, and examines various multivariate data visualization techniques that have been applied to microarray data analysis.
Journal ArticleDOI
Tree index of uncertain graphs
TL;DR: A concept of treeIndex of uncertain graph is proposed and a method to calculate tree index of uncertain graphs is given and a similar way to the treeindex of uncertain cycle and the path index of uncertainty graphs are proposed and analyzed.
Proceedings ArticleDOI
A Multi-Focus Image Fusion Algorithm with DT-CWT
TL;DR: Experimental results show that the algorithm proposed in this paper not only solves the problems such as low contrast and blocking effects caused by fusion algorithms in space domain, but also avoids the artifacts and ringing artifacts exhibited by conventional wavelet based fusion algorithms.
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.