Algorithms for scheduling malleable cloud tasks

Scheduling parallel tasks is a fundamental problem for many applications such as cloud computing. We consider the problem of scheduling a set of n deadline-sensitive parallel tasks on C machines. Each task is specified by a value, a workload, a deadline and a parallelism bound. The objective is to maximize the sum of values of jobs completed by their deadlines. For this problem, a greedy algorithm GreedyRTL (Jain et al., ACM SPAA 2012) was previously proposed and analyzed based on the dual fitting technique, achieving a performance guarantee (C-k)/C*(s-1)/s, where k and s are parameters specific to the tasks. In this paper, without recourse to the dual fitting technique, we propose a novel analysis technique for the greedy algorithms in the problem above. This technique enables improving the performance guarantee of GreedyRTL to min{(C-k+1)/C, (s-1)/s}. We then point out that (s-1)/s is the best performance guarantee that a general greedy algorithm can achieve. Based on the proposed analysis technique, we further derive the following algorithmic results: (1) an improved greedy algorithm achieving the performance guarantee (s-1)/s, (2) the first exact dynamic programming algorithm in the case where the set of possible task deadlines is finite, and (3) an exact algorithm for the machine minimization problem with the objective of minimizing the number of machines needed to schedule a set of tasks. The machine minimization problem is considered here for the first time under the model of this paper. The proposed analysis technique may have more applications.