The complexity of routing with few collisions

Till Fluschnik, Marco Morik, Manuel Sorge

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph G with two distinct terminal vertices and two positive integers p and k, the question is whether one can connect the terminals by at least p routes (e.g. paths) such that at most k edges are time-wise shared among them. We study three types of routes: traverse each vertex at most once (paths), each edge at most once (trails), or no such restrictions (walks). We prove that for paths and trails the problem is NP-complete on undirected and directed graphs even if k is constant or the maximum vertex degree in the input graph is constant. For walks, however, it is solvable in polynomial time on undirected graphs for arbitrary k and on directed graphs if k is constant. We additionally study for all route types a variant of the problem where the maximum length of a route is restricted by some given upper bound. We prove that this length-restricted variant has the same complexity classification with respect to paths and trails, but for walks it becomes NP-complete on undirected graphs.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 21st International Symposium, FCT 2017, Proceedings
EditorsMarc Zeitoun, Ralf Klasing
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783662557501
StatePublished - 1 Jan 2017
Event21st International Symposium on Fundamentals of Computation Theory, FCT 2017 - Bordeaux, France
Duration: 11 Sep 201713 Sep 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10472 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference21st International Symposium on Fundamentals of Computation Theory, FCT 2017

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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