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Uncertain graph management and analysis have attracted many research attentions. Among them, computing $k$ k -cores in uncertain graphs (aka, $(k,\eta)$ (k , η) -cores) is an important problem and has emerged in many applications such as community detection, protein-protein interaction network analysis and influence maximization. Given an uncertain graph, the $(k,\eta)$ (k , η) -cores can be derived by iteratively removing the vertex with an $\eta$ η -degree of less than $k$ k . However, the results heavily depend on the two input parameters $k$ k and $\eta$ η . The settings for these parameters are unique to the specific graph structure and the user's subjective requirements. In addition, computing and updating the $\eta$ η -degree for each vertex is the most costly component in the algorithm, and the cost is high. To overcome these drawbacks, we propose an index-based solution for computing $(k,\eta)$ (k , η) -cores. The size of the index is well bounded by $O(m)$ O (m) , where $m$ m is the number of edges in the graph. Based on the index, queries for any $k$ k and $\eta$ η can be answered in optimal time. We propose an algorithm for index construction with several different optimizations. We also propose a new algorithm for index construction in external memory. We conduct extensive experiments on eight real-world datasets to practically evaluate the performance of all proposed algorithms. [ABSTRACT FROM AUTHOR]

This article develops a practical framework for the multiobjective optimal planning of a grid-connected renewable-battery system considering a long-period operation. The capacities of wind turbine, solar photovoltaic (PV), and battery storage are optimized by minimizing three objective functions: cost of electricity (COE), grid dependence (GD), and total curtailed energy (TCE). A new rule-based energy management is developed for the long-period operation, where: 1) the capacity degradations of PV and battery are applied; 2) purchase and sell electricity prices are updated for each year using interest and escalation rates; and 3) the salvation value of the components is considered to achieve a realistic economic analysis of the planning problem. The developed multiobjective optimal planning model is examined using the long-period (ten years) real data of wind speed, solar insolation, ambient temperature, and load consumption for a grid-connected household in Australia. It is found that a household with the minimum GD (0.008%) results in a COE of 116 ¢/kWh with a TCE of 100 MWh in ten years. The proposed optimal planning framework based on the long-period operation is compared with the short-period operation. [ABSTRACT FROM AUTHOR]