A parametric critical path problem and an application for cyclic scheduling Original Research Article

The paper addresses a problem of finding critical paths in PERT networks (digraphs) with variable arc lengths depending on a parameter. By equipping the Bellman-Ford label-correcting algorithm with variable vectorial labels depending on the parameter, we derive its version that solves the problem in O(mn2) time, for all possible parameter values (where m stands for the number of arcs, and n is the number of nodes in the digraph). An application related to cyclic scheduling of tasks in a robotic cell is considered.