eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-03-09
6:1
6:16
10.4230/LIPIcs.STACS.2022.6
article
Approximability of Robust Network Design: The Directed Case
Al-Najjar, Yacine
1
2
Ben-Ameur, Walid
2
Leguay, Jérémie
1
Huawei Technologies, Paris Research Center, France
Samovar, Telecom SudParis, Institut Polytechnique de Paris, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol219-stacs2022/LIPIcs.STACS.2022.6/LIPIcs.STACS.2022.6.pdf
Robust Optimization
Network Design
Approximation
Inapproximability
Competitive Ratio of Oblivious Routing