obile devices (MDs), for example, smart phones and tablets, are becoming the major computing workspaces for individuals thanks to their increasing capabilities. Users expect to run desktop-level applications (e.g. document processing, media playback, and 3D gaming) on MDs anywhere. Specifically, a mobile application can consist of multiple tasks, which are termed mobile tasks. For instance, real-time rendering is a representative mobile task for 3D gaming on the MD. Although the capabilities of MDs keep increasing, executing resource-demanding mobile tasks on MDs would result in poor performance and short battery lifetime. A recent example is that the rendering capability requirement (in pixels per second) of mainstream desktop 3D gaming in 2012 is more than four times the rendering capability of the most powerful MDs in the same year, such as iPhone 5 [1]. One solution to the resource scarcity problem is to enable MDs to offload resource-demanding mobile tasks to surrogates, which are remote servers with stronger capabilities, through wireless networks [2]. As a result, the local resources on MDs can be reserved, and energy consumption can be reduced. Moreover, the emerging cloud computing technique can provide powerful Internet-based surrogates to help MDs [3].To offload the mobile task from a MD to an Internetbased surrogate, related data would be transferred between the MD and the surrogate through multiple layers of wired and wireless networks. For example, state-of-the-art cellular networks, such as long term evolution (LTE) systems [4], could serve as access networks for MDs to effectively offload mobile tasks. The process of mobile task offloading usually has a deadline to make MD users feel like running applications locally on their MDs. However, when multiple MDs in a cell offload mobile tasks, how to complete the offloading process before deadlines becomes a challenging issue. Specifically, the radio resources in a cell for data transmissions could be insufficient when a number of MDs offload mobile tasks, which would result in large communication latencies and degrade the MD user experience on the mobile task offloading significantly. As a result, it is crucial to effectively allocate radio resources to the data transmissions of the mobile task offloading from multiple MDs. Moreover, heterogenous requirements for mobile task offloading can be utilized to improve performance. Here, heterogenous requirements mean that the amount of data to be transferred between the MD and the surrogate, the surrogate response time, and the deadline of the mobile task offloading, could be different for different MDs.As motivated, we pose the radio resource allocation problem for the case that multiple MDs request mobile task offloading in a cell. Specifically, the purpose of radio resource allocation is to minimize the overall execution time for offloaded mobile tasks from multiple MDs, while satisfying the execution deadline for each mobile task. Moreover, the optimal radio resource allocation plan should take into acc...