An Approximation for Job Scheduling on Cloud with Synchronization and Slowdown Constraints

Cloud computing develops rapidly in recent years and provides service to many applications, in which job scheduling becomes more and more important to improve the quality of service. Parallel processing on cloud requires different machines starting simultaneously on the same job and brings processing slowdown due to communications overhead, defined as synchronization constraint and parallel slowdown. This paper investigates a new job scheduling problem of makespan minimization on uniform machines and identical machines with synchronization constraint and parallel slowdown. We first conduct complexity analysis proving that the problem is difficult in the face of adversarial job allocation. Then we propose a novel job scheduling algorithm, United Wrapping Scheduling (UWS), and prove that UWS admits an O(logm)-approximation for makespan minimization over m uniform machines. For the special case of identical machines, UWS is simplified to Sequential Allocation, Refilling and Immigration algorithm (SARI), proved to have a constant approximation ratio of 8 (tight up to a factor of 4). Performance evaluation implies that UWS and SARI have better makespan and realistic approximation ratio of 2 compared to baseline methods United-LPT and FIFO, and lower bounds.