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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TLDR
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
Citations
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Journal ArticleDOI
Percolation-like Scaling Exponents for Minimal Paths and Trees in the Stochastic Mean Field Model
TL;DR: The new exponents coincide with those recently found in a different context (comparing optimal and near-optimal solutions of the mean-field travelling salesman problem (TSP) and the minimum spanning tree (MST) problem), and reinforce the suggestion that scaling exponents determine universality classes for optimization problems on random points.
Journal ArticleDOI
Efficient tour planning for a measurement vehicle by combining next best view and traveling salesman
TL;DR: In this paper, a new variation of the Traveling Salesman Problem is proposed, referred to as the Explorational TSP (ETSP), which is the optimal tour with a minimum of observations.
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Task assignment in predictive maintenance for free-float bicycle sharing systems
TL;DR: In this article , the authors identify the role of black holes in accurate predictions of faulty bikes and propose two maintenance policies, i.e., the pooling model and the dedicated model, for the faulty bike maintenance assignment problem with the objective of minimizing the sum of maintenance time cost and travel time cost.
Journal ArticleDOI
Traveling salesman problem across well-connected cities and with location-dependent edge lengths
TL;DR: In this paper, the authors studied the convergence of the minimum weighted length cycle in the unconstrained case when the nodes are independently distributed throughout the unit square with location-dependent edge lengths.
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.
Book ChapterDOI
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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