License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2022.6
URN: urn:nbn:de:0030-drops-158165
URL: https://drops.dagstuhl.de/opus/volltexte/2022/15816/
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Al-Najjar, Yacine ; Ben-Ameur, Walid ; Leguay, Jérémie

Approximability of Robust Network Design: The Directed Case

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Abstract

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.

BibTeX - Entry

@InProceedings{alnajjar_et_al:LIPIcs.STACS.2022.6,
  author =	{Al-Najjar, Yacine and Ben-Ameur, Walid and Leguay, J\'{e}r\'{e}mie},
  title =	{{Approximability of Robust Network Design: The Directed Case}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15816},
  URN =		{urn:nbn:de:0030-drops-158165},
  doi =		{10.4230/LIPIcs.STACS.2022.6},
  annote =	{Keywords: Robust Optimization, Network Design, Approximation, Inapproximability, Competitive Ratio of Oblivious Routing}
}

Keywords: Robust Optimization, Network Design, Approximation, Inapproximability, Competitive Ratio of Oblivious Routing
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022


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