An asymptotically exact algorithm for the maximum traveling salesman problem in a finite-dimensional normed space

2011 ◽  
Vol 5 (2) ◽  
pp. 296-300 ◽  
Author(s):  
V. V. Shenmaier
Keyword(s):  
Traveling Salesman Problem ◽  
Normed Space ◽  
Exact Algorithm ◽  
Traveling Salesman ◽  
Finite Dimensional ◽  
Maximum Traveling Salesman Problem ◽  
Dimensional Normed Space

Quotients of Essentially Euclidean Spaces

2019 ◽  
Vol 62 (1) ◽  
pp. 71-74
Author(s):  
Tadeusz Figiel ◽  
William Johnson
Keyword(s):  
Normed Space ◽  
Quotient Space ◽  
Euclidean Spaces ◽  
Quantitative Version ◽  
Finite Dimensional ◽  
Dimensional Normed Space

AbstractA precise quantitative version of the following qualitative statement is proved: If a finite-dimensional normed space contains approximately Euclidean subspaces of all proportional dimensions, then every proportional dimensional quotient space has the same property.

scholarly journals The horofunction boundary of finite-dimensional normed spaces

2007 ◽  
Vol 142 (3) ◽  
pp. 497-507 ◽  
Author(s):  
CORMAC WALSH
Keyword(s):  
Unit Ball ◽  
Normed Space ◽  
Normed Spaces ◽  
Finite Dimensional ◽  
Dimensional Normed Space

AbstractWe determine the set of Busemann points of an arbitrary finite-dimensional normed space. These are the points of the horofunction boundary that are the limits of “almost-geodesics”. We prove that all points in the horofunction boundary are Busemann points if and only if the set of extreme sets of the dual unit ball is closed in the Painlevé–Kuratowski topology.

An exact algorithm for the Traveling Salesman Problem with Deliveries and Collections

Networks ◽  
2003 ◽  
Vol 42 (1) ◽  
pp. 26-41 ◽  
Author(s):  
R. Baldacci ◽  
E. Hadjiconstantinou ◽  
A. Mingozzi
Keyword(s):  
Traveling Salesman Problem ◽  
Exact Algorithm ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

Time-dependent asymmetric traveling salesman problem with time windows: Properties and an exact algorithm

2019 ◽  
Vol 261 ◽  
pp. 28-39 ◽  
Author(s):  
Anna Arigliano ◽  
Gianpaolo Ghiani ◽  
Antonio Grieco ◽  
Emanuela Guerriero ◽  
Isaac Plana
Keyword(s):  
Traveling Salesman Problem ◽  
Time Windows ◽  
Exact Algorithm ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Asymmetric Traveling Salesman Problem

scholarly journals Maximum average distance in complex finite dimensional normed spaces

2002 ◽  
Vol 66 (1) ◽  
pp. 125-134
Author(s):  
Juan C. García-Vázquez ◽  
Rafael Villa
Keyword(s):  
Unit Sphere ◽  
Metric Space ◽  
Normed Space ◽  
Average Distance ◽  
Complex Case ◽  
Normed Spaces ◽  
Finite Dimensional ◽  
Real Normed Space ◽  
Dimensional Normed Space

A number r > 0 is called a rendezvous number for a metric space (M, d) if for any n ∈ ℕ and any x1,…xn ∈ M, there exists x ∈ M such that . A rendezvous number for a normed space X is a rendezvous number for its unit sphere. A surprising theorem due to O. Gross states that every finite dimensional normed space has one and only one average number, denoted by r (X). In a recent paper, A. Hinrichs solves a conjecture raised by R. Wolf. He proves that for any n-dimensional real normed space. In this paper, we prove the analogous inequality in the complex case for n ≥ 3.

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