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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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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Automatic routing and scheduling of a fleet of vehicles providing door-to-door service for handicapped people
TL;DR: An unpublished algorithm which has been recently implemented to control by computer a fleet of vehicles providing a door-to-door service for handicapped people in Brussels is presented and the extension of the algorithm to the real time allotment is considered.
Journal ArticleDOI
Minimum Cost Multiobjective Programming Model for Target Efficiency in Sample Selection
Yousaf Shad Muhammad,Saima Khan,Ijaz Hussain,Alaa Mohamd Shoukry,Sadaf Shamsuddin,Showkat Gani +5 more
TL;DR: A model which elaborates relationship among efficiency of an estimator and survey cost and the resultant model is a multiobjective compromise allocation goal programming model, based on a multi objective optimization programming structure.
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Fifty years of operational research: 1972–2022
TL;DR: In July 2022, I received the EURO Gold medal at the 32nd EURO Conference held in Espoo, Finland as mentioned in this paper , which was based on the presentation I made at the medal award ceremony.
Posted Content
Rates of convergence of means of Euclidean functionals
Yooyoung Koo,Sungchul Lee +1 more
TL;DR: In this article, it was shown that for Euclidean functional with power-weighted edges, the rate of convergence to a finite constant is bounded by the sum of the lengths of the edges in minimal spanning trees, traveling salesman tours and minimal matchings.
The Probabilistic Minimum Spanning Tree, Part II: Probabilistic Analysis and Asymptotic Results
TL;DR: Probabilistic analysis under the random Euclidean and the random length models of the probabilistic minimum spanning tree (PMST) problem and the two re-optimization strategies adds evidence that a priori strategies may offer a useful and practical method for resolving combinatorial optimization problems on modified instances.
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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