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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 capabilityfor resource-constrained IoT devices. Computation offloading has recently received considerableattention in edge computing. Many existing studies have investigated the computation offloadingproblem with independent computing tasks. However, due to the inter-task dependency in variousdevices that commonly happens in IoT systems, achieving energy-efficient computation offloadingdecisions remains a challengeable problem. In this paper, a cloud-assisted edge computing frameworkwith a three-tier network in an IoT environment is introduced. In this framework, we first formulatedan energy consumption minimization problem as a mixed integer programming problem consideringtwo 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 ComputationOffloading (ECTCO) algorithm based on a semidefinite relaxation and stochastic mapping approachto obtain strategies of tasks computation offloading for IoT sensors. Simulation results demonstratedthat the cloud-assisted edge computing framework was feasible and the proposed ECTCO algorithmcould effectively reduce the energy cost of IoT sensors.