Finding Temporal Paths Under Waiting Time Constraints

Abstract Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, study paths temporal graphs, that is, graphs where vertex set fixed but edge changes over time, gained more and attention. A time-respecting, or , if it uses edges with non-decreasing time stamps. We investigate basic constraint for paths, spent at each must not exceed given duration $$\varDelta $$ ? referred to as - restless . This arises naturally modeling real-world processes like packet routing communication networks infection transmission routes diseases recovery confers lasting resistance. While finding without waiting restrictions known be doable polynomial we show “restless variant” this problem becomes computationally hard even very restrictive settings. For example, W[1]-hard when parameterized by distance disjoint underlying graph, which implies W[1]-hardness many other parameters feedback number pathwidth. natural question thus whether tractable some explore several parameterizations, presenting FPT algorithms three kinds parameters: (1) output-related (here, maximum length path), (2) classical applied (e.g., number), (3) new parameter called timed captures finer-grained features input may interest beyond work.