Linear Algorithms for Preemptive Scheduling of Multiprocessor Tasks Subject to Minimal Lateness

n scheduling theory it is widely assumed that a task is to be processed on one processor at a time. This assumption is not so obvious in the context of recently emerging parallel computer systems and parallel algorithms. In this work we consider tasks requiring more than one dedicated processor at a time, i.e. sets of processors simultaneously. Linear time algorithms will be given for the case of two, three and four processors and the Lmax criterion. The algorithms are based on the same simple paradigm. In some cases they deliver optimal solutions. In other cases, optimality is not guaranteed but they can still be used as fast approximation algorithms for which the worst case performance bounds are given. Results of the computational experiments involving four processors are reported.