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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Journal ArticleDOI
Artificial electric field algorithm with inertia and repulsion for spherical minimum spanning tree
TL;DR: The IRAEFA algorithm introduces the inertia mechanism and the repulsion between charges, expands the search space, increases the diversity of population, balances the exploration and development ability of the algorithm, and avoids the algorithm falling into the local optimal solution.
Proceedings ArticleDOI
Light Euclidean Spanners with Steiner Points
Hung Le,Shay Solomon +1 more
TL;DR: In this article, a Steiner spanners with lightness O(e^{-1} log Δ, where Δ is the spread of the point set, was constructed in polynomially bounded spread, where O_e hides a factor of poly(1/(e).
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A Probabilistic Analysis of the Capacitated Facility Location Problem
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Proceedings ArticleDOI
Multi-robot Scheduling and Path-Planning for Non-overlapping Operator Attention
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Proceedings ArticleDOI
Imaging applications of stochastic minimal graphs
TL;DR: The stochastic graph approach to entropy estimation is reviewed, convergence rates to that of plug-in estimators are compared, and a geo-registration application is discussed.
References
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On the shortest spanning subtree of a graph and the traveling salesman problem
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Solution of a Large-Scale Traveling-Salesman Problem
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