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
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DissertationDOI
Collision-free path planning for robots using B-splines and simulated annealing
TL;DR: In this paper, a two-link planar manipulator is used to obtain an optimal collision-free path for an AGV and/or robot in two and three dimensions by synthesizing a B-spline curve under geometric and intrinsic constraints.
Journal ArticleDOI
John Michael Hammersley. 21 March 1920 — 2 May 2004
Geoffrey Grimmett,Dominic Welsh +1 more
TL;DR: John Hammersley was a pioneer among mathematicians, who defied classification as pure or applied; when introduced to guests at Trinity College, Oxford, he would say he did ‘difficult sums’.
The Competitiveness of Commercial Electric Vehicles in the LTL Delivery Industry: A Model and Application
Brian Davis,Miguel A. Figliozzi +1 more
TL;DR: In this article, a cost minimization model, a model to calculate the power consumption and maximum potential range of an electric or conventional truck as a function of average velocity and weight, and a continuous approximation model to estimate fleet size, distance traveled, and ensure that practical routing constraints are satisfied.
Proceedings ArticleDOI
An asymptotic approximation of the traveling salesman problem with uniform non-overlapping time windows
TL;DR: In this article, a continuous asymptotic approximation of the traveling salesman problem with time windows in the Euclidean plane is presented, based on the well-known Beardwood-Halton-Hemmersley theorem.
Journal ArticleDOI
Asymptotic properties of combinatorial optimization problems in p -adic space
TL;DR: In this article, the authors considered the case where n points are randomly distributed in a unit p-adic ball of dimension d and investigated an asymptotic behavior of their solutions at large number of n.
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.
Journal ArticleDOI