Fog computing emerges as a promising mode to meet the stringent requirement of low latency in industrial Internet of Things (IIoT). By offloading partial computation-intensive tasks from fog node to cloud server, the computation experience of users can be further improved in fog computing system. In this paper, we develop an energy-efficient computation offloading scheme for IIoT in fog computing scenario. The purpose is to minimize energy consumption when computation tasks are accomplished within a desired energy overhead and delay. It has a comprehensive consideration on the components of energy consumption at fog node, which includes the energy consumption of local computing, transmitting and waiting states. To address this energy minimization problem, an accelerated gradient algorithm is proposed, it can find the optimal offloading ratio with a fast speed that improves the convergence speed of traditional method. Finally, the numerical results reveal that the proposed offloading scheme is superior to the local computing and full offloading schemes in terms of energy consumption and completion time, and further confirm the advantage of convergence rate.

Tensor decomposition is a fundamental tool for multiway data analysis. While most decomposition algorithms operate a collection of static data and perform batch processes, many applications produce data in a streaming manner - every time a subset of entries are generated, and previously seen entries cannot be revisited. In such scenarios, traditional decomposition approaches will be inappropriate, because they cannot provide timely updates when new data come in, and they need to access the whole dataset many times for batch optimization. To address this issue, we propose POST, a PrObabilistic Streaming Tensor decomposition algorithm, which enables real-time updates and predictions upon receiving new tensor entries, and supports dynamic growth of all the modes. Compared with the state-of-the-art streaming decomposition approach MAST, POST is more flexible in that it can handle arbitrary orders of streaming entries, and hence is more widely applicable. In addition, as a Bayesian inference algorithm, POST can quantify the uncertainty of the latent embeddings via their posterior distributions, and the confidence levels of the missing entry value predictions. On several real-world datasets, POST exhibits better or comparable predictive performance than MAST and other static decomposition algorithms.