Scaling hypothesis for the Euclidean bipartite matching problem

02/27/2014
by   Sergio Caracciolo, et al.
0

We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic prediction of the large N limit of the average cost in dimension d=1,2 and of the subleading correction in higher dimension. A non-trivial scaling exponent, γ_d=d-2/d, which differs from the monopartite's one, is found for the subleading correction. We argue that the same scaling holds true for a generic cost exponent in dimension d>2.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/19/2022

Algorithms for the Euclidean Bipartite Edge Cover Problem

Given a graph G=(V,E) with costs on its edges, the minimum-cost edge cov...
research
04/07/2019

The Penalty in Scaling Exponent for Polar Codes is Analytically Approximated by the Golden Ratio

The polarization process of conventional polar codes in binary erasure c...
research
10/25/2017

An information scaling law: ζ= 3/4

Consider the entropy of a unit Gaussian convolved over a discrete set of...
research
04/15/2022

Finding Hall blockers by matrix scaling

For a given nonnegative matrix A=(A_ij), the matrix scaling problem asks...
research
06/10/2012

Comments on "On Approximating Euclidean Metrics by Weighted t-Cost Distances in Arbitrary Dimension"

Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) rece...
research
02/27/2020

Scaling exponents saturate in three-dimensional isotropic turbulence

From a database of direct numerical simulations of homogeneous and isotr...
research
10/29/2019

Meta Distribution of SIR in Ultra-Dense Networks with Bipartite Euclidean Matchings

Ultra-dense networks maximise spatial spectral efficiency through spatia...

Please sign up or login with your details

Forgot password? Click here to reset