Journal ArticleDOI
The shortest path through many points
Jillian Beardwood,John H. Halton,J. M. Hammersley +2 more
- Vol. 55, Iss: 4, pp 299-327
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In this paper, it was shown that the length of the shortest closed path through n points in a bounded plane region of area v is almost always asymptotically proportional to √(nv) for large n; and this result was extended to bounded Lebesgue sets in k-dimensional Euclidean space.Abstract:
We prove that the length of the shortest closed path through n points in a bounded plane region of area v is ‘almost always’ asymptotically proportional to √(nv) for large n; and we extend this result to bounded Lebesgue sets in k–dimensional Euclidean space. The constants of proportionality depend only upon the dimensionality of the space, and are independent of the shape of the region. We give numerical bounds for these constants for various values of k; and we estimate the constant in the particular case k = 2. The results are relevant to the travelling-salesman problem, Steiner's street network problem, and the Loberman—Weinberger wiring problem. They have possible generalizations in the direction of Plateau's problem and Douglas' problem.read more
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Recent Advances in Applied Probability
TL;DR: Recent Advances in Applied Probability as mentioned in this paper is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography and linguistics.
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Green supply chain planning considering consumer’s transportation process
TL;DR: A two-step solution method for exact solutions to minimize the cost or maximize the profit is designed and the results show that a carbon cap will do more good than harm for the environment.
Journal ArticleDOI
On A Random Directed Spanning Tree
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Evolution of Athletic Records: Statistical Effects versus Real Improvements
TL;DR: From record estimation approach to the prediction of the maximum body length of humans for a specified size of a population respectively population group from a representative sample, formulae can be used to show that athletic records continue to improve with time, even if athletic performance remains constant.
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Random Geometric Problems on [0, 1]²
TL;DR: This paper presents some heuristics for the problem of the Minimal linear arrangement on [0,1]2 and concludes with a collection of open problems for graphs on random geometric models.
References
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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.
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Solution of a Large-Scale Traveling-Salesman Problem
TL;DR: The RAND Corporation in the early 1950s contained Arrow, Bellman, Dantzig, Flood, Ford, Fulkerson, Gale, Johnson, Nash, Orchard-Hays, Robinson, Shapley, Simon, Wagner, and other household names as discussed by the authors.
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