Throughput Maximization for Speed-Scaling with Agreeable Deadlines

We are given a set of n jobs and a single processor that can vary its speed dynamically. Each job J j is characterized by its processing requirement (work) p j , its release date r j and its deadline d j . We are also given a budget of energy E and we study the scheduling problem of maximizing the throughput (i.e. the number of jobs which are completed on time). We show that the problem can be solved by dynamic programming when all the jobs are released at the same time in O(n 4 logn logP), where P is the sum of the processing requirements of the jobs. For the more general case of agreeable deadlines, where the jobs can be ordered such that for every i < j, both r i ≤ r j and d i ≤ d j , we propose a dynamic programming algorithm solving the problem optimally in O(n 6 logn logP). In addition, we consider the weighted case where every job j is also associated with a weight w j and we are interested in maximizing the weighted throughput. For this case, we prove that the problem becomes \({\cal NP}\)-hard in the ordinary sense and we propose a pseudo-polynomial time algorithm.