Online Matching in Sparse Random Graphs: Non-Asymptotic Performances of Greedy Algorithm
Nathan Noiry, Vianney Perchet, Flore Sentenac
Abstract
Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed degree distributions -- the so-called configuration model. We estimate the competitive ratio of the simplest algorithm, GREEDY, by approximating some relevant stochastic discrete processes by their continuous counterparts, that are solutions of an explicit system of partial differential equations. This technique gives precise bounds on the estimation errors, with arbitrarily high probability as the problem size increases. In particular, it allows the formal comparison between different configuration models. We also prove that, quite surprisingly, GREEDY can have better performance guarantees than RANKING, another celebrated algorithm for online matching that usually outperforms the former.
BibTeX
@inproceedings{
noiry2021online,
title={Online Matching in Sparse Random Graphs: Non-Asymptotic Performances of Greedy Algorithm},
author={Nathan Noiry and Vianney Perchet and Flore Sentenac},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=TZ0eEqEBRA}
}