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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An ant colony optimization technique for solving min–max Multi-Depot Vehicle Routing Problem
TL;DR: An extension of an existing ant-colony technique for solving the Single Depot Vehicle Routing Problem (SDVRP) to solve the multiple depots and min–max variants of the problem is presented.
Journal ArticleDOI
Variable Density Sampling with Continuous Trajectories
TL;DR: This paper discusses the choice of an optimal sampling subspace (smallest subset) allowing perfect reconstruction of sparse signals and shows that a mixed strategy involving partial deterministic sampling and independent drawings can help breaking the so-called "coherence barrier".
Journal ArticleDOI
Analysis of an O(N2) heuristic for the single vehicle many-to-many Euclidean dial-a-ride problem
TL;DR: An O(N2) heuristic is developed to solve the single vehicle many-to-many Euclidean Dial-A-Ride problem based on the Minimum Spanning Tree of the modes of the problem, which exhibits statistical stability over a broad range of problem sizes.
Journal ArticleDOI
Performance and Design of Mobility Allowance Shuttle Transit Services: Bounds on the Maximum Longitudinal Velocity
TL;DR: Bounds on the maximum longitudinal velocity are developed to evaluate the performance and help the design of mobility allowance shuttle transit (MAST) services and can be helpful in theDesign of MAST systems to set the main parameters of the service, such as slack time and headway.
Book ChapterDOI
Experimental analysis of algorithms
TL;DR: It is shown that simulation can provide a useful, general tool for developing new understanding of algorithms and principles for successful experimental research in this domain are developed.
References
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Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
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