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- GABRIELE SICURO
- 2014

In 1781 a French geometer, Gaspard Monge (1746–1818), published his Mémoire sur la théorie des déblais at des remblais, in which he discussed the following very simple problem. Let us suppose that we have a certain number of mines and the same number of deposits. We want to associate each mine to one deposit only (where the production of the considered mine… (More)

The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e., the optimal matching problem between points randomly distributed on a d-dimensional Euclidean space, where the cost to minimize depends on the… (More)

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… (More)

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