A fixed-parameter algorithm for scheduling unit dependent tasks on parallel machines with time windows

This paper proves that the existence of a feasible schedule for set dependent tasks unit execution times with release dates and deadlines on limited number processors is fixed-parameter tractable problem. The parameter considered pathwidth interval graph associated time windows tasks. A algorithm based dynamic programming approach developed proved to solve this decision Fixed-parameter algorithms two classical problems P|prec,pi=1,ri|Cmax P|prec,pi=1,ri|Lmax are then derived using binary search. They are, as far we know, first these scheduling problems.