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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A correction algorithm for token-passing sequences in mobile communication networks
Yaron I. Gold,Shlomo Moran +1 more
TL;DR: A distributed approximation algorithm for the Traveling Salesman Problem (TSP) in networks that use a broadcast, multiaccess communication channel and is capable of taking advantage of certain node layouts to reduce the cost of computing the path.
Journal ArticleDOI
Big is Green, Procompetitive, and Saves Lives: The Economics of Route Consolidation
Evaluation eines Verschmelzungsalgorithmus für Lösungen des Handlungsreisendenproblems
TL;DR: In this paper, a vergleichsweise neuer Ansatz stellt jedoch das Kombinieren vorhandener Losungen dar, in which Kantenmengen gegebener Handlungsreisendertouren als Ausgangsbasis fur weitere Optimierungen verwendet.
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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