Scheduling precedence-constrained tasks is a classical problem that has been
studied for more than fifty years. However, little progress has been made in
the setting where there are communication delays between tasks. Results for the
case of identical machines were derived nearly thirty years ago, and yet no
results for related machines have followed. In this work, we propose a new
scheduler, Generalized Earliest Time First (GETF), and provide the first
provable, worst-case approximation guarantees for the goals of minimizing both
the makespan and total weighted completion time of tasks with precedence
constraints on related machines with machine-dependent communication times
