General non-approximability results in presence of hierarchical communications

Abstract

We investigate the problem of minimizing the makespan (resp. the sum of the completion time) for the multiprocessor scheduling problem in presence of hierarchical communications. We consider a model with two levels of communication: interprocessor and intercluster. The processors are grouped in connected clusters. We propose general non-approximability results for the case where all the tasks of the precedence graph have unit execution times, where the multiprocessor is composed of an unrestricted number of machines with /spl lscr/ /spl ges/ 4 identical processors each.