On Maximizing the Throughput of Multiprocessor Tasks

We consider the problem of scheduling n independent multiprocessor tasks with due dates and unit processing times, where the objective is to compute a schedule minimizing the throughput. We derive the complexity results and present several approximation algorithms. For the parallel variant of the problem, we introduce the first-fit increasing algorithm and the latest first increasing algorithm, and prove that their approximation guarantees are 2 and 2 1=m, respectively (m 2 is the number of processors). Then we propose a revised algorithm with the worst-case ratio bounded by 3=2. For the dedicated variant, we present a simple greedy algorithm. We show that its worst-case ratio is bounded by p m+1. We straighten this result showing that the problem with common due date D= 1 cannot be approximated within a factor of m1=2 ε nor for any ε> 0, unless NP=ZPP.