Chromatic Scheduling of 1- and 2-Processor UET Tasks on Dedicated Machines with Availability Constraints

We address a generalization of the classical 1and 2-processor UET scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these constraints we show that the problem of optimal scheduling of sparse instances can be solved in polynomial time.