Existing dependent task offloading approaches mainly rely on centralized algorithms and are typically constrained to single-objective optimization. In addition, offloading fairness among fog servers remains insufficiently addressed. To tackle these challenges, this paper proposes a novel distributed method that integrates Gale–Shapley Matching (GSM) with Improved Particle Swarm Optimization (IPSO), whose goal is to maximize the offloading gain on the user side and the fairness on the fog server side. Specifically, we firstly formulate an offloading gain maximization problem for dependent task offloading in multi-user and multi-fog computing scenarios, where the offloading gain is defined by jointly optimizing energy consumption and latency of task offloading. Then, we propose a GSM preference list construction method that considers user offloading gain, the number of offloading acceptances by fog servers and channel quality. Finally, GSM is employed to achieve stable user–fog associations, and IPSO is applied to optimize subtask offloading decisions. Experimental results show that, compared with existing algorithms, this method increases the average offloading gain by 9%; and improves the average fairness by 16.6% with minimal loss of user offloading gain. Therefore, the proposed algorithm can jointly optimize the latency and energy consumption of user tasks while ensuring excellent long-term fairness among fog servers.

Data sharing in the Industrial Internet of Things (IIoT) can increase productivity and reduce costs, but it is critical to ensure data security while sharing data. Secure multi-party computation (MPC) can address security problems such as data leakage during computation. However, it still faces the risk of malicious behavior from internal participants and the problem of sharing data decision-making. To address these problems, we propose a Game Theory-based secure Multi-Party Computation scheme for IIoT Data (GTMPC). Firstly, we design a traceable, verifiable and auditable industrial data sharing and computing framework for the IIoT based on blockchain. Then, we propose an MPC protocol that can resist malicious behavior from participants. It obtains the voting results through voting identifiers and multi-party multiplication. More importantly, we establish the revenue optimization models of data sharing between consumers and computing devices. Based on the above models, we model the MPC interaction-sharing process between consumers and computing devices as a Stackelberg game, and use the backward induction method to prove that there is a unique Stackelberg Equilibrium in the game. Furthermore, we also propose an MPC-solving algorithm based on the Steepest Descent Method (MPC_SDM), and obtain the optimal industrial data sharing scheme and calculation results according to the constantly updated credit score. Finally, the simulation experiment results show that the MPC_SDM algorithm is efficient and feasible in IIoT, better than the comparison algorithm, and the revenue can be increased by 13.2%.

How to jointly optimize task offloading and resource allocation to minimize the task failure rate and task payments remains an unresolved challenge in fog networks. Focusing on this problem, this research formulates a novel task offloading and resource allocation model with two offloading modes and on-demand virtual resource units (VRUs). This model is decomposed into two sub-problems to solve: a joint task offloading and resource allocation optimization problem and a matching problem with externalities and dynamics. First, for a given terminal node (TN) and fog node (FN), this research theoretically derives the optimal offloading ratio and resource allocation strategy to minimize the payment of TNs for two offloading modes, i.e., immediate and queued offloading. Second, in the multi-TNs and multi-FNs scenario, the problem of making the task offloading decision is transformed into a many-to-one matching game by considering externalities and dynamics. Finally, a Deferred acceptance-based Loss ratio and Payment Minimized task Offloading and resource Allocation optimization (DLPMOA) algorithm is proposed to derive a stable and Pareto-optimal match. The simulation results show that the proposed DLPMOA has better performance in terms of task failure rate, task average payment, fog computing resource utilization, and fairness than the state-of-the-art methods.

In the fog network composed of dense terminal devices and fog servers, how to reduce the system energy consumption during task offloading is a challenging problem. To solve this problem, this article first formulates the energy consumption minimization problem of partial task offloading under delay constraints with dynamic voltage scaling (DVS) and transmission power control (TPC) techniques. Second, this problem was decomposed into two subproblems to solve: 1) the partial task offloading problem with optimal energy consumption under known matching between the terminal device and fog server and 2) the optimal matching problem between terminal devices and fog servers. For the first subproblem, the optimal solution is obtained through theoretical derivation, and the EOPCO-S algorithm is proposed to solve it. For the second subproblem, we transform the original problem into a weighted bipartite graph matching problem and propose the Kuhn–Munkres-based EOPCO-M algorithm to solve it. Finally, numerical simulations are carried out to verify the theoretical derivation and the effectiveness of the proposed algorithms. Experimental results show that the proposed algorithm can significantly reduce the energy consumption of fog networks compared with several baseline algorithms.

In space target monitoring system, due to the interference of noise, stray light and the limitations of the image acquisition system, there are nonuniform background and smear phenomena in star images. Moreover, there are also a large number of background stars in star images. All these factors lead to the difficulty of space target detection. In order to improve the detection performance, an adaptive space target detection algorithm is proposed in this letter. Firstly, in order to suppress the complex background interference in the star image, a window adaptive bidirectional one-dimensional (1-D) median filtering method is proposed, whose window size is set based on the maximum star size in the first star image. Then, background correction is performed by bidirectional 1-D median filter. Secondly, in order to improve the reliability of space target segmentation, an improved inter-frame difference method is proposed, which consists of two parts: 1) the bright line residue is eliminated based on a horizontal 1-D median filter; 2) the target segmentation threshold is adaptively set based on the Kalman filter method. Compared with existing algorithms, our proposed method can detect space targets quickly with low false alarm rate and high detection rate under complex background conditions.