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
Mechanism for Connecting Input Edges Using Steiner Tree
Joon Mo Kim,In Bum Kim +1 more
TL;DR: In experiments, a mechanism connecting all input edges with minimum length through Steiner tree made connection length decrease, while building time for a connecting solution increase average 192.0% comparing with the method using minimum spanning tree, which shows the mechanism might be well applied to the applications where connecting cost is more important than building time of connecting solution.
Proceedings ArticleDOI
The optimization of pipeline network based on parent genetic algorithms
Wang Hua,Jiang Yifeng,Wang Yan +2 more
TL;DR: The single parent genetic algorithm is used to solve minimum spanning tree to get a group solution, from which many factors can be synthetically considered, and the practical application displays the efficiency and effectiveness of this approach.
Journal ArticleDOI
Ga-based alternative approaches for the degree-constrained spanning tree problem
TL;DR: The degree-constrained minimum spanning tree (dc-MST) problem is of high practical importance and there are few effective algorithms to solve this problem because of its NP-hard complexity.
Journal ArticleDOI
A Survey on Task Allocation and Scheduling in Robotic Network Systems
TL;DR: In this article , the authors provide a comprehensive overview of task allocation and scheduling strategies and related metrics suitable for robotic network cloud systems and discuss the issues related to allocation and task scheduling methods and the limitations that need to be overcome.
Book ChapterDOI
On Transforming Unit Cube into Tree by One-Point Mutation
Zbigniew Pliszka,Olgierd Unold +1 more
TL;DR: This work is presenting new properties of vertices of a dimensional unit cube obtained after mutually unambiguous (bijective) transformation of these vertice of a cube into a tree.
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.