Interference-free walks in time: temporally disjoint paths
| Autor: | Nina Klobas, George B. Mertzios, Rolf Niedermeier, Hendrik Molter, Philipp Zschoche |
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| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Discrete mathematics Vertex (graph theory) Computational complexity theory Computer science Parameterized complexity Monotonic function Disjoint sets Discrete time and continuous time Artificial Intelligence Computer Science - Data Structures and Algorithms Path (graph theory) FOS: Mathematics Mathematics - Combinatorics Data Structures and Algorithms (cs.DS) Combinatorics (math.CO) Constant (mathematics) MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | 30th International Joint Conference on Artificial Intelligence (IJCAI-21), Montreal, Quebec, 21-26 Aug 2021 [Conference proceedings] IJCAI |
| ISSN: | 1573-7454 1387-2532 |
| DOI: | 10.1007/s10458-022-09583-5 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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