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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Thermostatistical persistency: A powerful improving concept for simulated annealing algorithms
TL;DR: In this paper, an extension of the simulated annealing algorithm is proposed to solve the traveling salesman problem and the minimisation of an unconstrained 0-1 quadratic function.
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Probabilistic analysis of the held and Karp lower bound for the euclidean traveling salesman problem
TL;DR: It is proved that, if n points are identically and independently distributed according to a distribution with bounded support and absolutely continuous part fxdx over the d-cube, the Held-Karp lower bound on these n points is almost surely asymptotic to βHKdn d-1/d â« fx d- 1/d dx.
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On the solutions of stochastic traveling salesman problems
TL;DR: In this paper, the authors considered the n-city traveling salesman problem where the distances between the cities are non-deterministic and estimated the expectation of the length of the optimal tour.
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Estimating the regional mean status and change of soil properties: two distinct objectives for soil survey
TL;DR: In this article, a simple process model of soil organic carbon in soils of lowland tropical forest is used to examine the problem of resampling to estimate change in soil, and the expected advantages of paired sampling for change and the very different sampling requirements that may pertain for inventory and monitoring.
Journal ArticleDOI
Probabilistic exchange algorithms and Euclidean traveling salesman problems
TL;DR: In this paper, the role of Gibbs distribution in simulated annealing is studied, convergence conditions are reviewed and some new results shown, and results of extensive empirical studies of the method on various Euclidean traveling salesman problems are given.
References
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Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
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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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