The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
The shortest path through many points
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.
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Cites
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Solution of a Large-Scale Traveling-Salesman Problem
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The Traveling-Salesman Problem
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Tables of functions with formulae and curves
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Formal Procedures for Connecting Terminals with a Minimum Total Wire Length
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Optimization by Simulated Annealing
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983) · Science · doi:10.1126/science.220.4598.671 · Cited by 45,134
An effective implementation of the Lin–Kernighan traveling salesman heuristic
Helsgaun, K. (2000) · European Journal of Operational Research · doi:10.1016/s0377-2217(99)00284-2 · Cited by 1,630
Colloquium : Quantum annealing and analog quantum computation
Das, A., & Chakrabarti, B. K. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1061 · Cited by 700
The ζ(2) limit in the random assignment problem
Aldous, D. J. (2001) · Random Structures & Algorithms · doi:10.1002/rsa.1015 · Cited by 278
On-Time Last-Mile Delivery: Order Assignment with Travel-Time Predictors
Liu, S., He, L., & Max Shen, Z.-J. (2021) · Management Science · doi:10.1287/mnsc.2020.3741 · Cited by 268
Metadata
- Authors
- Beardwood, J., Halton, J. H., & Hammersley, J. M.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1959-10
- Volume
- 55
- Issue
- 4
- Pages
- 299-327
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W2014068360
- Cited by
- 937
- References
- 11
- FWCI
- 10.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Beardwood, J., Halton, J. H., & Hammersley, J. M. (1959). The shortest path through many points. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100034095
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
