Complexity of scheduling of coupled tasks with chains precedence constraints and any constant length of gap
Klaus Ecker, Michal Tanas · Journal of the Operational Research Society · 2011
Coupled tasks scheduling was originally introduced for modelling complex radar devices. It is still used for controlling such devices and applied in similar applications. This paper considers a problem of coupled tasks scheduling on one processor, under the assumptions that all processing times are equal to 1, the gap has a constant exact length and the precedence constraints are strict. Although it is proven that the problem stated above is NP-hard in the strong sense if the precedence constraints have a form of a general graph, it is possible to solve some of its relaxed versions in polynomial time. This paper contains a solution for the problem of coupled tasks scheduling with an assumption that the precedence constraints graph has a form of chains and it presents an algorithm that can solve the problem with such assumption in time O(n log n).