New applications of the Muntz and Coffman algorithm

Muntz and Coffman proposed an algorithm to solve the problem of scheduling preemptable tasks either with arbitrary precedences on two processors, or tasks with tree-like precedences on an arbitrary number of processors, for the schedule length criterion. In this work, we demonstrate that this well-known algorithm has interesting features which extend its application to many other scheduling problems. Three deterministic scheduling problems for preemptable tasks are considered. Though these problems have diverse formulations, they have at least one thing in common: Basically their optimization algorithms boil down to the Muntz–Coffman algorithm. The foundations of the Muntz–Coffman algorithm versatility are established.