Scheduling tree-like task systems with non-uniform deadlines subject to unit-length communication delays

We consider the problem of scheduling outforests and inforests with non-uniform deadlines subject to unit-length communication delays. We will prove that minimum-tardiness schedules for outforests on two processors and for chain-like task systems on m processors can be constructed in polynomial time. In addition, we present two polynomial-time approximation algorithms: one with an asymptotic approximation bound of 2−2/m for scheduling outforests with non-positive deadlines on m processors and one with an asymptotic approximation bound of 2 for scheduling inforests with non-positive deadlines on m processors. Moreover, it is proved that for a special class of inforests, minimum-tardiness schedules on m processors can be constructed in polynomial time.