Congestion-Free Rerouting of Flows on DAGs

Authors Saeed Akhoondian Amiri, Szymon Dudycz, Stefan Schmid, Sebastian Wiederrecht

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Author Details

Saeed Akhoondian Amiri
  • Max-Planck Institute of Informatics, Germany
Szymon Dudycz
  • University of Wroclaw, Poland
Stefan Schmid
  • University of Vienna, Austria
Sebastian Wiederrecht
  • TU Berlin, Germany

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Saeed Akhoondian Amiri, Szymon Dudycz, Stefan Schmid, and Sebastian Wiederrecht. Congestion-Free Rerouting of Flows on DAGs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 143:1-143:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Changing a given configuration in a graph into another one is known as a reconfiguration problem. Such problems have recently received much interest in the context of algorithmic graph theory. We initiate the theoretical study of the following reconfiguration problem: How to reroute k unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner? This problem finds immediate applications, e.g., in traffic engineering in computer networks. We show that the problem is generally NP-hard already for k=2 flows, which motivates us to study rerouting on a most basic class of flow graphs, namely DAGs. Interestingly, we find that for general k, deciding whether an unsplittable multi-commodity flow rerouting schedule exists, is NP-hard even on DAGs. Our main contribution is a polynomial-time (fixed parameter tractable) algorithm to solve the route update problem for a bounded number of flows on DAGs. At the heart of our algorithm lies a novel decomposition of the flow network that allows us to express and resolve reconfiguration dependencies among flows.

Subject Classification

ACM Subject Classification
  • Networks → Network algorithms
  • Theory of computation → Network flows
  • Unsplittable Flows
  • Reconfiguration
  • DAGs
  • FPT
  • NP-Hardness


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