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
Reads0
Chats0
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
More filters
Book ChapterDOI
A Simple and Quick Approximation Algorithm for Traveling Salesman Problem in the Plane
TL;DR: This work presents a quite simple, fast and practical algorithm to find a short cyclic tour that visits a set of points distributed on the plane and shows that the algorithm is a 'probabilistic' constant-ratio approximation algorithm for uniform random distributions.
Graph-based Estimation of Information Divergence Functions
TL;DR: A new divergence measure, the Dp-divergence, is introduced that can be estimated directly from samples without parametric assumptions on the distribution and bounds the binary, cross-domain, and multi-class Bayes error rates and, in certain cases, provides provably tighter bounds than the Hellinger divergence.
Posted Content
On the Nearest Neighbor Algorithm for Mean Field Traveling Salesman Problem
TL;DR: It is shown that under some conditions on $F$, which are satisfied by exponential distribution with constant mean, the total length of the nearest neighbor tour, asymptotically almost surely scales as $\log n$.
Journal ArticleDOI
The physicist's approach to the travelling salesman problem-II
TL;DR: In this paper, a criterion based on numerical evidence is given for the choice of the number of stripes in the stripe approximation to the traveling salesman problem, and asymptotic convergence results for the length of the stripes approximation using martingale difference methods are given.
References
More filters
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.
Journal ArticleDOI