We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal matching configuration. In the other one, on the contrary, such a link is forbidden. Both problems have the same asymptotic average optimal cost of the random-link matching problem on the complete graph. Using a replica approach and previous results of Wastlund (2010 Acta Mathematica 204 91-150), we analytically derive the finite-size corrections to the asymptotic optimal cost. We compare our results with numerical simulations and we discuss the main differences between random-link fractional matching problems and the random-link matching problem.

The random fractional matching problem

Lucibello Carlo;MALATESTA, ENRICO MARIA;
2018

Abstract

We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we allow each node to be linked to itself in the optimal matching configuration. In the other one, on the contrary, such a link is forbidden. Both problems have the same asymptotic average optimal cost of the random-link matching problem on the complete graph. Using a replica approach and previous results of Wastlund (2010 Acta Mathematica 204 91-150), we analytically derive the finite-size corrections to the asymptotic optimal cost. We compare our results with numerical simulations and we discuss the main differences between random-link fractional matching problems and the random-link matching problem.
2018
2018
Lucibello, Carlo; Malatesta, ENRICO MARIA; Parisi, Giorgio; Sicuro, Gabriele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4020240
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