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
Reads0
Chats0
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
More filters
Book ChapterDOI
On the History of Combinatorial Optimization (Till 1960)
TL;DR: A history of combinatorial optimization can be found in this article, where the assignment problem was formulated as a linear programming problem that automatically has an integer optimum solution. But it was only recently that it was shown that minimizing a linear functional over the set of doubly stochastic matrices gives a permutation matrix, being the optimum assignment.
Journal ArticleDOI
Dynamic Vehicle Routing for Robotic Systems
TL;DR: This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process.
Journal ArticleDOI
Coordinated Logistics with a Truck and a Drone
John Gunnar Carlsson,Siyuan Song +1 more
TL;DR: It is demonstrated that the improvement in efficiency of a delivery system in which an unmanned aerial vehicle UAV provides service to customers while making return trips to a truck that is itself moving is proportional to the square root of the ratio of the speeds of the truck and the UAV.
Journal ArticleDOI
Percolation Processes and Related Topics
H. L. Frisch,J. M. Hammersley +1 more
TL;DR: A general review of the current state of the theory of percolation processes and related topics can be found in this paper, where a wide variety of examples drawn from physics, chemistry, biology, engineering and communication theory of problems which can profitably be considered special instances of a Percolation process are discussed.
Journal ArticleDOI
Retail Store Density and the Cost of Greenhouse Gas Emissions
TL;DR: A model of the retail supply chain is presented that includes operating costs such as fuel and rent for floor space as well as a cost for environmental externalities associated with carbon emissions.
References
More filters
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