# Online Matching in Sparse Random Graphs: Non-Asymptotic Performances of Greedy Algorithm

arXiv: https://arxiv.org/abs/2107.00995 · HTML: https://mlsanity.com/paper/2107.00995/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 39 references that are in the map.
- First posted on arXiv 2 Jul 2021.

## Builds on (most cited first, 2 of 2)

- [Greedy Online Bipartite Matching on Random Graphs](https://mlsanity.com/paper/1307.2536/) (2013)
- [Greedy Bipartite Matching in Random Type Poisson Arrival Model](https://mlsanity.com/paper/1805.00578/) (2018)

## Built on by (most cited first, 2 of 2)

- [(Optimal) Online Bipartite Matching with Degree Information](https://mlsanity.com/paper/2110.11439/) (2021)
- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)

## Abstract (arXiv)

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.