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
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Reducing Latency In Data Delivery In Wireless Sensor Network With Mobile Elements
Rachana K,B. Chempavathy +1 more
TL;DR: A stop and wait disk covering (SWDC) scheme and a multi-hop SWDP scheme which jointly optimizes the sink trajectory and the packet routing paths are proposed.
Book ChapterDOI
Probabilistic analysis of some travelling salesman heuristics
TL;DR: It is shown that the probability that the tour length produced by this heuristic exceeds any fixed percentage of the expected tour length goes to zero when n tends to infinity.
Optimizing Task Waiting Times in Dynamic Vehicle Routing
Alexander Botros,Barry J. Gilhuly,Nils Wilde,Armin Sadeghi,Javier Alonso-Mora,Delft University of Technology +5 more
TL;DR: In this paper , the authors study the problem of deploying a fleet of mobile robots to service tasks that arrive stochastically over time and at random locations in an environment, where quality of service can be improved by prioritizing long-waiting tasks.
Book ChapterDOI
Towards Asymptotically Optimal One-to-One PDP Algorithms for Capacity 2+ Vehicles
TL;DR: In this paper, the authors considered the one-to-one Pickup and Delivery Problem (PDP) in Euclidean Space with arbitrary dimension d, where n transportation requests are picked i.i.d. with a separate origin-destination pair for each object to be moved.
Deriving route lengths from radial distances: Empirical evidence
TL;DR: In this article, the authors estimate expected route lengths for multi-drop trips (serving several destinations) from radial distances (as the crow flies) to avoid actual vehicle routing, e.g. in transportation studies at a strategic level.
References
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Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
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