info:eu-repo/semantics/article
Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
Fecha
2021-01Registro en:
Jonckheere, Matthieu Thimothy Samson; Sáenz, Manuel; Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs; Elsevier Science; Stochastic Processes And Their Applications; 131; 1-2021; 122-150
0304-4149
1879-209X
CONICET Digital
CONICET
Autor
Jonckheere, Matthieu Thimothy Samson
Sáenz, Manuel
Resumen
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 Erdös–Rényi 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.