Interference-free walks in time: temporally disjoint paths

Nina Klobas, George B. Mertzios, Hendrik Molter, Rolf Niedermeier, Philipp Zschoche

Research output: Contribution to journalArticlepeer-review


We investigate the computational complexity of finding temporally disjoint paths and walks in temporal graphs. There, the edge set changes over discrete time steps. Temporal paths and walks use edges that appear at monotonically increasing time steps. Two paths (or walks) are temporally disjoint if they never visit the same vertex at the same time; otherwise, they interfere. This reflects applications in robotics, traffic routing, or finding safe pathways in dynamically changing networks. At one extreme, we show that on general graphs the problem is computationally hard. The path version is NP-hard even if we want to find only two temporally disjoint paths. The walk version is W-hard (Klobas in IJCAI 4090–4096, 2021) when parameterized by the number of walks. However, it is polynomial-time solvable for any constant number of walks. At the other extreme, restricting the input temporal graph to have a path as underlying graph, quite counter-intuitively, we find NP-hardness in general but also identify natural tractable cases.

Original languageEnglish
Article number1
JournalAutonomous Agents and Multi-Agent Systems
Issue number1
StatePublished - 1 Jun 2023


  • NP-complete problem
  • Parameterized complexity
  • polynomial-time algorithm
  • Temporal graph
  • Temporal path

ASJC Scopus subject areas

  • Artificial Intelligence


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