TY - GEN
T1 - Online Matching in Sparse Random Graphs
T2 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
AU - Noiry, Nathan
AU - Sentenac, Flore
AU - Perchet, Vianney
N1 - Publisher Copyright:
© 2021 Neural information processing systems foundation. All rights reserved.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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, which 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, GREEDYcan have better performance guarantees than RANKING, another celebrated algorithm for online matching that usually outperforms the former.
AB - 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, which 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, GREEDYcan have better performance guarantees than RANKING, another celebrated algorithm for online matching that usually outperforms the former.
UR - https://www.scopus.com/pages/publications/85126681677
M3 - Conference contribution
AN - SCOPUS:85126681677
T3 - Advances in Neural Information Processing Systems
SP - 21400
EP - 21412
BT - Advances in Neural Information Processing Systems 34 - 35th Conference on Neural Information Processing Systems, NeurIPS 2021
A2 - Ranzato, Marc'Aurelio
A2 - Beygelzimer, Alina
A2 - Dauphin, Yann
A2 - Liang, Percy S.
A2 - Wortman Vaughan, Jenn
PB - Neural information processing systems foundation
Y2 - 6 December 2021 through 14 December 2021
ER -