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Fast Re-Routing in Networks: On the Complexity of Perfect Resilience

Authors Matthias Bentert , Esra Ceylan , Valentin Hübner , Stefan Schmid , Jiří Srba

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Subject Classification

ACM Subject Classification
  • Networks → Network protocol design
  • Networks → Network properties
  • Theory of computation → Problems, reductions and completeness
Keywords
  • routing in computer networks
  • fast re-route
  • perfect resilience
  • complexity

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Abstract

To achieve fast recovery from link failures, most modern communication networks feature fully decentralized fast re-routing mechanisms. These re-routing mechanisms rely on pre-installed static re-routing rules at the nodes (the routers), which depend only on local failure information, namely on the failed links incident to the node. Ideally, a network is perfectly resilient: the re-routing rules ensure that packets are always successfully routed to their destinations as long as the source and the destination are still physically connected in the underlying network after the failures. Unfortunately, there are examples where achieving perfect resilience is not possible. Surprisingly, only very little is known about the algorithmic aspect of when and how perfect resilience can be achieved. 
We investigate the computational complexity of analyzing such local fast re-routing mechanisms. Our main result is a negative one: we show that even checking whether a given set of static re-routing rules ensures perfect resilience is coNP-complete. Additionally, we investigate other fundamental variations of the problem. In particular, we show that our coNP-completeness proof also applies to scenarios where the re-routing rules have specific patterns (known as skipping in the literature). 
On the positive side, for scenarios where nodes do not have information about the link from which a packet arrived (the so-called in-port), we present a linear-time algorithm to realize perfect resilience whenever possible (which we show can also be determined in linear time).

Cite As Get BibTex

Matthias Bentert, Esra Ceylan, Valentin Hübner, Stefan Schmid, and Jiří Srba. Fast Re-Routing in Networks: On the Complexity of Perfect Resilience. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.OPODIS.2025.31

Author Details

Matthias Bentert
  • University of Bergen, Norway
  • TU Berlin, Germany
Esra Ceylan
  • TU Berlin, Germany
  • Institute of Science and Technology Austria, Klosterneuburg, Austria
Valentin Hübner
  • Institute of Science and Technology Austria, Klosterneuburg, Austria
Stefan Schmid
  • TU Berlin, Germany
Jiří Srba
  • Aalborg University, Denmark

Funding

  • Bentert, Matthias: ERC Horizon 2020 research and innovation programme (grant agreement No. 819416) and ERC Consolidator grant AdjustNet (agreement No. 864228).
  • Ceylan, Esra: German Research Foundation (DFG) project ReNO, Schwerpunktprogramm: Resilienz in Vernetzten Welten - Beherrschen von Fehlern, Überlast, Angriffen und dem Unbekannten (SPP 2378).
  • Schmid, Stefan: German Research Foundation (DFG) project ReNO, Schwerpunktprogramm: Resilienz in Vernetzten Welten - Beherrschen von Fehlern, Überlast, Angriffen und dem Unbekannten (SPP 2378).

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