The Random Fractional Matching Problem
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 W\"{a}stlund [Acta Mathematica 204, 91-150 (2010)], 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.
Keywords
Cite
@article{arxiv.1802.02997,
title = {The Random Fractional Matching Problem},
author = {Carlo Lucibello and Enrico M. Malatesta and Giorgio Parisi and Gabriele Sicuro},
journal= {arXiv preprint arXiv:1802.02997},
year = {2018}
}
Comments
24 pages, 3 figures