2-hop labeling has been widely utilized to accelerate the efficiency of online shortest distance queries. Given the nature of frequent changes in real-world graphs, the efficient maintenance of 2-hop labeling index has been extensively studied recently. However, existing methods cannot efficiently process large-scale graphs due to their high time and memory costs, and most of them process large batches of updates sequentially, significantly decreasing efficiency. In this paper, we propose a novel algorithm for maintaining the 2-hop labeling index in a parallel manner, called M2HL , which can efficiently handle both edge insertions and deletions. Moreover, we theoretically prove that M2HL maintains both correctness and minimality for the updated 2-hop labeling index. Our experiments on ten large-scale graphs demonstrate that M2HL outperforms the state-of-the-art 2-hop labeling maintenance methods by up to four orders of magnitude in speed while maintaining correctness and minimality, as well as exhibiting strong scalability and low memory usage.

Time-series forecasting is an important problem across a wide range of domains. Designing accurate and prompt forecasting algorithms is a non-trivial task, as temporal data that arise in real applications often involve both non-linear dynamics and linear dependencies, and always have some mixtures of sequential and periodic patterns, such as daily, weekly repetitions, and so on. At this point, however, most recent deep models often use Recurrent Neural Networks (RNNs) to capture these temporal patterns, which is hard to parallelize and not fast enough for real-world applications especially when a huge amount of user requests are coming. Recently, CNNs have demonstrated significant advantages for sequence modeling tasks over the de-facto RNNs, while providing high computational efficiency due to the inherent parallelism. In this work, we propose HyDCNN, a novel hybrid framework based on fully Dilated CNN for time-series forecasting tasks. The core component in HyDCNN is a proposed hybrid module, in which our proposed position-aware dilated CNNs are utilized to capture the sequential non-linear dynamics and an autoregressive model is leveraged to capture the sequential linear dependencies. To further capture the periodic temporal patterns, a novel hop scheme is introduced in the hybrid module. HyDCNN is then composed of multiple hybrid modules to capture the sequential and periodic patterns. Each of these hybrid modules targets on either the sequential pattern or one kind of periodic patterns. Extensive experiments on five real-world datasets have shown that the proposed HyDCNN is better compared with state-of-the-art baselines and is at least 200% better than RNN baselines. The datasets and source code will be published in Github to facilitate more future work.