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As an emerging and promising computing paradigm in the Internet of things (IoT), edge computing can significantly reduce energy consumption and enhance computation capability for resource-constrained IoT devices. Computation offloading has recently received considerable attention in edge computing. Many existing studies have investigated the computation offloading problem with independent computing tasks. However, due to the inter-task dependency in various devices that commonly happens in IoT systems, achieving energy-efficient computation offloading decisions remains a challengeable problem. In this paper, a cloud-assisted edge computing framework with a three-tier network in an IoT environment is introduced. In this framework, we first formulated an energy consumption minimization problem as a mixed integer programming problem considering two constraints, the task-dependency requirement and the completion time deadline of the IoT service. To address this problem, we then proposed an Energy-efficient Collaborative Task Computation Offloading (ECTCO) algorithm based on a semidefinite relaxation and stochastic mapping approach to obtain strategies of tasks computation offloading for IoT sensors. Simulation results demonstrated that the cloud-assisted edge computing framework was feasible and the proposed ECTCO algorithm could effectively reduce the energy cost of IoT sensors.