Abstract
Online monitoring user cardinalities (or degrees) in graph streams is fundamental for many applications. For example in a bipartite graph representing user-website visiting activities, user cardinalities (the number of distinct visited websites) are monitored to report network anomalies. These real-world graph streams may contain user-item duplicates and have a huge number of distinct user-item pairs, therefore, it is infeasible to exactly compute user cardinalities when memory and computation resources are limited. Existing methods are designed to approximately estimate user cardinalities, whose accuracy highly depends on parameters that are not easy to set. Moreover, these methods cannot provide anytime-available estimation, as the user cardinalities are computed at the end of the data stream. Real-time applications such as anomaly detection require that user cardinalities are estimated on the fly. To address these problems, we develop novel bit and register sharing algorithms, which use a bit array and a register array to build a compact sketch of all users' connected items respectively. Compared with previous bit and register sharing methods, our algorithms exploit the dynamic properties of the bit and register arrays (e.g., the fraction of zero bits in the bit array at each time) to significantly improve the estimation accuracy, and have low time complexity (0(1)) to update the estimations each time they observe a new user item pair. In addition, our algorithms are simple and easy to use, without requirements to tune any parameter. We evaluate the performance of our methods on real-world datasets. The experimental results demonstrate that our methods are several times more accurate and faster than state-of-the-art methods using the same amount of memory.