基于顺序的堆芯维护简化算法
Simplified Algorithms for Order-Based Core Maintenance
摘要：
图分析吸引了研究和行业社区的广泛关注。由于$k$ -core分解的线性时间复杂度，它被广泛应用于生物学、社交网络、社区发现、生态学、信息传播等领域。在许多这样的应用中，数据图随时间连续变化。这些更改对应于边的插入和删除。我们研究如何有效地维护$k$ -core，而不是重新计算$k$ -core，这是耗时的。也就是说，当插入或删除边时，我们需要通过搜索更多的顶点来识别受影响的顶点。最先进的基于顺序的方法在所有顶点之间保持一个顺序，即所谓的$k$顺序，这可以显著减少搜索空间。然而，这种基于顺序的方法是复杂的理解和实现，其正确性没有正式讨论。在这项工作中，我们提出了一个简化的顺序为基础的方法，通过引入经典的顺序数据结构，以保持$k$顺序，这显着提高了最坏情况下的时间复杂度的边缘插入和删除算法。此外，我们的简化方法是直观的理解和实现，它是很容易证明的正确性正式。此外，我们讨论了一个简化的批量插入方法。实验评估我们的简化方法超过12个真实的和合成的图与数十亿的顶点。与现有的方法相比，我们的简化方法实现了高加速高达7.7倍和9.7倍的边缘插入和删除，分别。
英文摘要：
Graph analytics attract much attention from both research and industry communities. Due to the linear time complexity, the $k$-core decomposition is widely used in many real-world applications such as biology, social networks, community detection, ecology, and information spreading. In many such applications, the data graphs continuously change over time. The changes correspond to edge insertion and removal. Instead of recomputing the $k$-core, which is time-consuming, we study how to maintain the $k$-core efficiently. That is, when inserting or deleting an edge, we need to identify the affected vertices by searching for more vertices. The state-of-the-art order-based method maintains an order, the so-called $k$-order, among all vertices, which can significantly reduce the searching space. However, this order-based method is complicated for understanding and implementation, and its correctness is not formally discussed. In this work, we propose a simplified order-based approach by introducing the classical Order Data Structure to maintain the $k$-order, which significantly improves the worst-case time complexity for both edge insertion and removal algorithms. Also, our simplified method is intuitive to understand and implement; it is easy to argue the correctness formally. Additionally, we discuss a simplified batch insertion approach. The experiments evaluate our simplified method over 12 real and synthetic graphs with billions of vertices. Compared with the existing method, our simplified approach achieves high speedups up to 7.7x and 9.7x for edge insertion and removal, respectively.
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