{"type":"ScholarlyArticle","title":"Interference-free Walks in Time: Temporally Disjoint Paths","authors":[{"name":"Nina Klobas","slug":"nina-klobas","given":"Nina","family":"Klobas","affiliation":""},{"name":"George B. Mertzios","slug":"george-b-mertzios","given":"George B.","family":"Mertzios","affiliation":""},{"name":"Hendrik Molter","slug":"hendrik-molter","given":"Hendrik","family":"Molter","affiliation":""},{"name":"Rolf Niedermeier","slug":"rolf-niedermeier","given":"Rolf","family":"Niedermeier","affiliation":""},{"name":"Philipp Zschoche","slug":"philipp-zschoche","given":"Philipp","family":"Zschoche","affiliation":""}],"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.\r\n\r\nOn 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.","doi":"10.24963/ijcai.2021/563","url":"https://ijcai.org/proceedings/2021/563","pdf":"https://ijcai.org/proceedings/2021/0563.pdf","markdown":"https://ijcai.org/proceedings/2021/563.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/563","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Planning and Scheduling","track":"Main Track","number":563,"pages":{"first":4090,"last":4096},"keywords":["Agent-based and Multi-agent Systems: Multi-agent Planning","Planning and Scheduling: Planning and Scheduling","Planning and Scheduling: Scheduling"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}