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
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Dissertation
Quadratic Bottleneck Problems: Algorithms, complexity and related topics.
TL;DR: This thesis studies the quadratic bottleneck combinatorial optimization problem (QBCOP) which generalizes the well-known class of bottleneck problems and identifies polynomially solvable special cases and develops heuristic algorithms.
Posted Content
Universal Data Reduction and Network Sparsification Method By Minimal Algorithmic Information Loss
TL;DR: It is demonstrated numerically that the unsupervised, Minimal Information Loss Sparsification (MILS) method is robust, has the potential to maximize the preservation of all recursively enumerable features in data and networks, and achieves equal to significantly better results than other data reduction and network sparsification methods.
Book ChapterDOI
Searching for Order
TL;DR: The Ngandong skulls are a group of fossilized human skulls discovered in 1931 in the Solo River valley on the island of Java, Indonesia as discussed by the authors , and are considered to be remains of hominids of the species Homo erectus.
Reference EntryDOI
Minimum Spanning Trees
TL;DR: Two classical algorithms are discussed: Prim's algorithm and Kruskal's algorithm, followed by recent developments that improve the asymptotic time bounds using advanced data structures.
Book ChapterDOI
Greed Is Good? Prove It!
TL;DR: So-called greedy algorithms are short-sighted, in that they make each choice in isolation, doing what looks good right here, right now.
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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.