Multi-phase algorithms for throughput maximization for real-time scheduling (Q1587588)

The following scheduling problem is considered: given are \(n\) jobs, and \(m\) machines. To each job \(i\), a profit \(w_i\), a release date \(r_i\), and a deadline \(d_i\) is associated, \(1 \leq i \leq n\). Further, for each job \(i\) and machine \(j\), there is a length \(l_{ij}\), \(1 \leq i \leq n\), \(1 \leq j \leq m\). The problem is to find a maximum-weight feasible schedule, where a schedule is called feasible if no preemption occurs and two jobs on a same machine are not allowed to overlap. The authors provide combinatorial approximation algorithms for this problem and various special cases of it. In particular, a 2-approximation algorithm for the general case is described.