Approximation schemes for scheduling and covering on unrelated machines

We examine the problem of assigning n independent jobs to m unrelated parallel machines, so that each job is processed without interruption on one of the machines, and at any time, every machine processes at most one job. We focus on the case where m is a fixed constant, and present a new rounding approach that yields approximation schemes for multi-objective minimum makespan scheduling with a fixed number of linear cost constraints. The same approach gives approximation schemes for covering problems like maximizing the minimum load on any machine, and for assigning specific or equal loads to the machines.