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The search for the shortest paths in some real-world networks with high complexity, essential for practical applications such as map navigation, makes it convenient to consider the influences of dynamic multi-layer and multi-layer networks on the various mathematical models of such networks. In this paper, exact algorithms are presented to accelerate and improve the efficiency of path planning in complex network structures and changing scenarios, thus improving service performance. In particular, Layers and Cross-network Distance Matrices (L C D M) method for calculating the shortest path length in multi-layer networks is introduced, the accuracy of which is illustrated with examples and simulations. Through the relationship between the number of cross-nodes and the complexity of L C D M algorithm, we propose the layer sub-network detection processes of large-scale single-layer networks. It is similar to community detection, which makes the application of L C D M algorithm more extensive. In addition, the LCDM-based D L C D M (Dynamic Layers and Cross-network Distance Matrices) algorithm for calculating the shortest path length is introduced. A general case shows the accuracy and the change trend of the shortest path over time. And D L C D M algorithm direct application to the Beijing bus network is shown as a 11-layer network which, by integrating real-time traffic conditions, enables route planning to respond to traffic jams more flexibly and provide the shortest route based on current traffic conditions, providing drivers with a smoother and more reliable driving experience. [ABSTRACT FROM AUTHOR]

Public key encryption is an important method to ensure data security. In recent years, researchers have designed multiple certificateless encryption (CLE) schemes, and the security proofs of most known schemes are done in random oracle model (ROM). It is generally known that the standard model (SM) is more reliable than the ROM. Currently, there are only three CLE schemes with provable security in SM. Unfortunately, all three schemes require pairing operations, enjoy high computation costs, and are not suitable for mobile devices. In this paper, we constructed a new CLE scheme. Compared with other schemes, the new scheme is with two advantages: First, the security proofs of the new scheme are done in SM. Second, the new scheme does not use pairing operation and enjoys higher computation efficiency. Efficiency analysis shows that the computation cost of the new scheme is only 12.4% of that of the most efficient scheme known, which is suitable for mobile devices. [ABSTRACT FROM AUTHOR]

Network resilience, measuring the degree of network performance decline and recovery capacity after perturbation onset, is highly related to capability against a cascading failure. However, the network resilience assessment and reinforcement strategy remain challenging for the network with a potential cascade risk. In this paper, we propose three resilience reinforcement strategies based on the nodal capacity redundancy at the different structure scales and develop a network resilience assessment method considering both the structure and nodal load. The performance of the reinforcement strategy has a close correlation with the nodal capacity redundancy, which performs as the node with larger capacity redundancy is reinforced, the better reinforcement efficiency. Moreover, the heterogeneity of the nodal load profoundly affects the reinforcement efficiency. To enhance network resilience, the reinforcement strategies proposed are then improved based on the optimization theory. Theoretical analysis and experiments for both the Barabási-Albert scale-free network and Erdős-Rényi random network under various initial conditions demonstrate that the modified reinforcement strategy outperforms existing methods in terms of the reinforcement efficiency. This paper provides a general paradigm to address the potential cascade risk, which will enable us to design more resilient networks against cascading failures. • The resilience reinforcement strategies based on the nodal capacity redundancy are proposed. • Network resilience is evaluated in terms of the cascading and recovery process. • The reinforcement efficiency is relevant to the heterogeneity of the nodal load. • The resilience reinforcement strategy is improved based on optimization theory. [ABSTRACT FROM AUTHOR]