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 nontrivial scaling exponent, γd=d−2d, 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.
Scaling hypothesis for the Euclidean bipartite matching problem / S. Caracciolo, C. Lucibello, G. Parisi, G. Sicuro. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 90:1(2014 Jul 21), pp. 012118.1-012118.9.
Scaling hypothesis for the Euclidean bipartite matching problem
S. CaraccioloPrimo
;
2014
Abstract
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 nontrivial scaling exponent, γd=d−2d, 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.Pubblicazioni consigliate
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