Routing with Congestion in Acyclic Digraphs

Authors Saeed Akhoondian Amiri, Stephan Kreutzer, Dániel Marx, Roman Rabinovich

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Saeed Akhoondian Amiri
Stephan Kreutzer
Dániel Marx
Roman Rabinovich

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Saeed Akhoondian Amiri, Stephan Kreutzer, Dániel Marx, and Roman Rabinovich. Routing with Congestion in Acyclic Digraphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 7:1-7:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We study the version of the k-disjoint paths problem where k demand pairs (s_1,t_1), ..., (s_k,t_k) are specified in the input and the paths in the solution are allowed to intersect, but such that no vertex is on more than c paths. We show that on directed acyclic graphs the problem is solvable in time n^{O(d)} if we allow congestion k-d for k paths. Furthermore, we show that, under a suitable complexity theoretic assumption, the problem cannot be solved in time f(k)n^{o(d*log(d))} for any computable function f.
  • algorithms
  • disjoint paths
  • congestion
  • acyclic digraphs
  • XP
  • W[1]-hard


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