Multiprocessor Scheduling with Availability Constraints

Abstract

We consider the problem of scheduling a given set of tasks on multiple processors with predefined periods of unavailability, with the aim of minimizing the maximum completion time. Since this problem is strongly NP-hard, polynomial approximation algorithms are being studied for its solution. Among these, the best known are LPT (largest processing time first) and Multifit with their variants. We give a Multifit-based algorithm, FFDL Multifit, which has an optimal worstcase performance in the class of polynomial algorithms for same-speed processors with at most two downtimes on each machine, and for uniform processors with at most one downtime on each machine, assuming that P = N P. Our algorithm finishes within 3/2 the maximum between the end of the last downtime and the end of the 5 Example showing that the 3/2 bound is asymptotically tight. .. .. 22 CHAPTER I

Approximation for Scheduling on Parallel Machines with Fixed Jobs or Unavailability Periods

“…In [28], a very long proof is outlined that LMULTIFIT achieves a worst-case approximation bound of 1.5 when scheduling on identical processors with at most two fixed jobs on each machine. In [29], an algorithm using two MULTIFIT-like algorithms is shown to have a worst-case approximation bound of 1.625, which likely can be improved to 1.6 without excessive effort.…”

“…Sometimes it is enough to define the partial order only using the number of processors [11], while in most cases, it is useful to include multiple characteristics of problem instances, such as all or a part of the characteristics enumerated above. In one situation, a minimal counterexample was defined to also have minimal job lengths, meaning that if in a minimal counterexample the length of one job is reduced, the resulting instance is not a counterexample [28].…”