Approximability of robust network design: the directed case - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2022

Approximability of robust network design: the directed case

Résumé

We consider robust network design problems where an uncertain traffic vector belonging to a polytope has to be dynamically routed to minimize either the network congestion or some linear reservation cost. We focus on the variant in which the underlying graph is directed. We prove that an O(√ k) = O(n)-approximation can be obtained by solving the problem under static routing, where k is the number of commodities and n is the number of nodes. This improves previous results of Hajiaghayi et al. [SODA'2005] and matches the Ω(n) lower bound of Ene et al. [STOC'2016] and the Ω(√ k) lower bound of Azar et al. [STOC'2003]. Finally, we introduce a slightly more general problem version where some flow restrictions can be added. We show that it cannot be approximated within a ratio of k c log log k (resp. n c log log n) for some constant c. Making use of a weaker complexity assumption, we prove that there is no approximation within a factor of 2 log 1−ϵ k (resp. 2 log 1−ϵ n) for any ϵ > 0.
Fichier principal
Vignette du fichier
LIPIcs-STACS-2022-6.pdf (1.34 Mo) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-03953268 , version 1 (23-01-2023)

Licence

Identifiants

Citer

Yacine Al-Najjar, Walid Ben-Ameur, Jérémie Leguay. Approximability of robust network design: the directed case. The 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022), Mar 2022, Marseille, France. pp.6:1-6:16, ⟨10.4230/LIPIcs.STACS.2022.6⟩. ⟨hal-03953268⟩
15 Consultations
16 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More