# Average-case complexity of a branch-and-bound algorithm for maximum independent set, under the $\mathcal{G}(n,p)$ random model

Abstract : We study average-case complexity of branch-and-bound for maximum independent set in random graphs under the $\mathcal{G}(n,p)$ distribution. In this model every pair $(u,v)$ of vertices belongs to $E$ with probability $p$ independently on the existence of any other edge. We make a precise case analysis, providing phase transitions between subexponential and exponential complexities depending on the probability $p$ of the random model.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01258958
Contributor : Marie-Annick Guillemer Connect in order to contact the contributor
Submitted on : Tuesday, January 19, 2016 - 4:49:56 PM
Last modification on : Thursday, January 20, 2022 - 9:02:01 AM

### Identifiers

• HAL Id : hal-01258958, version 1
• ARXIV : 1505.04969

### Citation

Nicolas Bourgeois, Rémi Catellier, T. Denat, V. Th. Paschos. Average-case complexity of a branch-and-bound algorithm for maximum independent set, under the $\mathcal{G}(n,p)$ random model. 2015. ⟨hal-01258958⟩

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