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Edge computing has become a popular computing paradigm to offload delay-sensitive tasks from mobile devices (MDs) to edge servers. However, due to the limited computation resources, edge computing may fail to support the increasing amount of data. In this paper, we consider a collaborative edge and cloud computing network. For delay-sensitive tasks, two optimization problems are formulated: 1) Quantity driven problem that aims to maximize the number of served MDs; 2) Energy driven problem that aims to minimize energy consumption. Both are mixed-integer nonlinear programming problems that are NP-hard. To derive the optimal task offloading decisions, a binary tree based task offloading (BTTO) scheme is proposed. By leveraging the convex optimization and branch-and-bound method, an alternating optimization (AO) approach is presented to obtain high-quality solutions. A detailed convergence …