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
On estimating the distribution of optimal traveling salesman tour lengths using heuristics
Vikrant Vig,Udatta S. Palekar +1 more
TL;DR: Some empirical results based on Monte Carlo simulations for the symmetric Euclidean and Rectilinear TSPs are presented and it is shown that a Beta distribution gives excellent fits for small to moderate sized TSP problems.
Proceedings Article
Travelling salesman-based variable density sampling
TL;DR: In this paper, a traveling salesman problem solver is proposed to generate continuous sampling trajectories by drawing a small set of measurements independently and joining them using a travelling salesman solver.
Journal ArticleDOI
Spin glass, the travelling salesman problem, neural networks and all that
G. Venkataraman,G. Athithan +1 more
TL;DR: In this paper, the authors present an overview of diverse topics that are seemingly different but interrelated, with strong connections to statistical mechanics on the one hand and spin glass physics on the other.
Journal ArticleDOI
Fuzzy multi-objective optimization for optimum allocation in multivariate stratified sampling with quadratic cost and parabolic fuzzy numbers
Neha Gupta,Abdul Bari +1 more
TL;DR: The uncertain parameters of the problem, such as stratum standard deviations, measurement costs, travel costs and total budget of the survey are considered as parabolic fuzzy numbers and the problem is formulated as a fuzzy multi-objective nonlinear programming problem with quadratic cost function.
Posted Content
Generalised elastic nets
TL;DR: This paper generalises the elastic net model to an arbitrary quadratic tension term, e.g. derived from a discretised differential operator, and gives an efficient learning algorithm that applies not only to generalised elastic nets but also to other methods using discrete differential penalties.
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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