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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Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts : Towards Memetic Algorithms
TL;DR: In this paper, the authors present a short abstract, which is a summary of the paper.Short abstract, isn't it? But it is short abstracts, not abstracts.
Journal ArticleDOI
An effective implementation of the Lin–Kernighan traveling salesman heuristic
TL;DR: An implementation of the Lin–Kernighan heuristic, one of the most successful methods for generating optimal or near-optimal solutions for the symmetric traveling salesman problem (TSP), is described.
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Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
TL;DR: The previous best approximation algorithm for the problem (due to Christofides) achieves a 3/2-aproximation in polynomial time.
References
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Journal ArticleDOI
The Traveling-Salesman Problem
TL;DR: The traveling-salesman problem is that of finding a permutation P of the integers from 1 through n that minimizes the quantity A where the aαβ are a given set of real numbers.
Journal ArticleDOI
Formal Procedures for Connecting Terminals with a Minimum Total Wire Length
H. Loberman,A. Weinberger +1 more
TL;DR: Two methods for systematically selecting the shortest connections from a list of possible connections to obtain a minimum total wire length are presented, which will be called a minimum tree.
A sample survey of the acreage under jute in Bengal.
TL;DR: In this paper, a brief account of recent investigations regarding the application of the method of random samples for estimating the acreage under jute in Bengal has been given, where it is estimated that on an average about 85 per cent is grown in Bengal.