---
title: "Interference-free Walks in Time: Temporally Disjoint Paths"
authors:
  - "Nina Klobas"
  - "George B. Mertzios"
  - "Hendrik Molter"
  - "Rolf Niedermeier"
  - "Philipp Zschoche"
doi: "10.24963/ijcai.2021/563"
url: "https://ijcai.org/proceedings/2021/563"
pdf: "https://ijcai.org/proceedings/2021/0563.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "4090-4096"
track: "Main Track"
keywords:
  - "Agent-based and Multi-agent Systems: Multi-agent Planning"
  - "Planning and Scheduling: Planning and Scheduling"
  - "Planning and Scheduling: Scheduling"
---

# Interference-free Walks in Time: Temporally Disjoint Paths

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

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 4090-4096. DOI: [10.24963/ijcai.2021/563](https://doi.org/10.24963/ijcai.2021/563)

## Abstract

We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically increasing time steps. Two paths (or walks) are temporally disjoint if they never use 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.

On the one extreme, we show that on general graphs the problem is computationally hard. The "walk version" is W[1]-hard when parameterized by the number of routes. However, it is polynomial-time solvable for any constant number of walks. The "path version" remains NP-hard even if we want to find only two temporally disjoint paths. On the other extreme, restricting the input temporal graph to have a path as underlying graph, quite counterintuitively, we find NP-hardness in general but also identify natural tractable cases.