scholarly journals On the hardness of range assignment problems

Networks ◽  
2008 ◽  
Vol 52 (4) ◽  
pp. 183-195 ◽  
Author(s):  
Bernhard Fuchs
2010 ◽  
Vol 36 ◽  
pp. 239-246
Author(s):  
Frank Baumann ◽  
Christoph Buchheim

2014 ◽  
Vol 2 ◽  
pp. 362-365
Author(s):  
Akio Watanabe ◽  
Kaori Kuroda ◽  
Kantaro Fujiwara ◽  
Tohru Ikeguchi

2009 ◽  
Author(s):  
Michael Knörzer
Keyword(s):  

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.


2020 ◽  
Author(s):  
Irina Zaitseva ◽  
Oleg Malafeyev ◽  
Ekaterina Konopko ◽  
Viktoriya Taran ◽  
Anna Durakova

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