Within the paper, we study several variants of the decision problem, Scheduling with precedence constraints and time windows, denoted by P ∣ p r e c , r i , d i ∣ ⋆ , and present improved fixed-parameter algorithms parameterized by the maximum processing time p max and the maximum number μ of overlapping time windows, defined as μ = max t ∈ N | { i ∈ S ∣ r i ≤ t < d i } | . Firstly, we propose an algorithm for P ∣ p r e c , r i , d i ∣ ⋆ with time complexity O ( ( p max + 2 ) μ p max n 3 ) , where n is the number of tasks. This sig...
