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Elastic partitioning of computations between mobile devices and cloud is an important and challenging research topic for mobile cloud computing. Existing works focus on the single-user computation partitioning, which aims to optimize the application completion time for one particular single user. These works assume that the cloud always has enough resources to execute the computations immediately when they are offloaded to the cloud. However, this assumption does not hold for large scale mobile cloud applications. In these applications, due to the competition for cloud resources among a large number of users, the offloaded computations may be executed with certain scheduling delay on the cloud. Single user partitioning that does not take into account the scheduling delay on the cloud may yield significant performance degradation. In this paper, we study, for the first time, multi-user computation partitioning problem (MCPP), which considers the partitioning of multiple users’ computations together with the scheduling of offloaded computations on the cloud resources. Instead of pursuing the minimum application completion time for every single user, we aim to achieve minimum average completion time for all the users, based on the number of provisioned resources on the cloud. We show that MCPP is different from and more difficult than the classical job scheduling problems. We design an offline heuristic algorithm, namely SearchAdjust, to solve MCPP. We demonstrate through benchmarks that SearchAdjust outperforms both the single user partitioning approaches and classical job scheduling approaches by 10 percent on average in terms of application delay. Based on SearchAdjust, we also design an online algorithm for MCPP that can be easily deployed in practical systems. We validate the effectiveness of our online algorithm using real world load traces. [ABSTRACT FROM AUTHOR]