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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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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Zero-Change Netlist Transformations: A New Technique for Placement Benchmarking
Andrew B. Kahng,Sherief Reda +1 more
TL;DR: Methods that apply zero-change netlist transformations (ZCNTs) to synthesize netlists having typical netlist statistics are developed and an approach to estimate the suboptimality of other metrics, such as rectilinear minimum-spanning tree (RMST) and minimum-Steiner tree, is extended.
Book ChapterDOI
Chapter 6 Probabilistic networks and network algorithms
TL;DR: This chapter discusses probabilistic networks and network algorithms through more stylized stochastic models that provide mathematically tractable models of reasonable generality that can be used to explore a variety of different computational or estimation methods.
Journal ArticleDOI
Probabilistic Analysis of Assignment Ranking: The Traveling Salesman Problems
James R. Evans,Richard A. Hall +1 more
TL;DR: In this paper, the use of assignment ranking techniques for solving the traveling salesman problem is considered in a probabilistic framework, and the assumptions required for a valid mathematical analysis are discussed.
Integration Of Locational Decisions with the Household Activity Pattern Problem and Its Applications in Transportation Sustainability
TL;DR: In this paper, the authors focus on the integration of the Household Activity Pattern Problem (HAPP) with various locational decisions considering both supply and demand sides, and present several methods to merge these two distinct areas into an integrated framework that has been previously exogenously linked by feedback or equilibrium processes.
References
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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.
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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.
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