Cache-assisted ultra-dense mobile edge computing (MEC) networks are a promising solution for meeting the increasing demands of numerous Internet-of-Things mobile devices (IMDs). To address the complex interferences caused by small base stations (SBSs) deployed densely in such networks, this paper explores the combination of orthogonal frequency division multiple access (OFDMA), non-orthogonal multiple access (NOMA), and base station (BS) clustering. Additionally, security measures are introduced to protect IMDs' tasks offloaded to BSs from potential eavesdropping and malicious attacks. As for such a network framework, a computation offloading scheme is proposed to minimize IMDs' energy consumption while considering constraints such as delay, power, computing resources, and security costs, optimizing channel selections, task execution decisions, device associations, power controls, security service assignments, and computing resource allocations. To solve the formulated problem efficiently, we develop a further improved hierarchical adaptive search (FIHAS) algorithm, giving some insights into its parallel implementation, computation complexity, and convergence. Simulation results demonstrate that the proposed algorithms can achieve lower total energy consumption and delay compared to other algorithms when strict latency and cost constraints are imposed.
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