Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:131

Article

Jonckheere, Matthieu^1,2  Saenz, Manuel^1,2 

[1] Univ Buenos Aires, Inst Calculo, CONICET, Buenos Aires, DF, Argentina

[2] Univ Buenos Aires, Math Dept, FCEyN, Buenos Aires, DF, Argentina

关键词: Random graphs;    Sequential algorithms;    Maximum independent sets;    Hydrodynamic limits;   

DOI  :  10.1016/j.spa.2020.09.009

来源: Elsevier

【 摘 要 】

Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this algorithm to find an independent set of asymptotically optimal size in large sparse random graphs with given degree sequences. In the special case of sparse Erdos-Renyi graphs, our results allow to give a simple proof of the so-called e-phenomenon identified by Karp and Sipser for matchings and to give an alternative characterisation of the asymptotic independence number. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free