Approximating the throughput of multiple machines under real-time scheduling

We consider the following fundamental scheduling problem. The input to the problem consists of n jobs and k machines. Each of the jobs is associated with a release time, a deadline, a weight, and a processing time on each of the machines. The goal is to find a schedule that maximizes the weight of jobs that meet their deadline. We give constant factor approximation algorithms for four variants of the problem, depending on the type of the machines (identical vs. unrelated), and the weight of the jobs (identical vs. arbitrary). All these variants are known to be NP-Hard, and we observe that the two variants involving unrelated machines are also MAX-SNP hard. To the best of our knowledge, these are the first approximation algorithms for such problems in the non-preemptive off-line setting.