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Online monitoring user cardinalities (or degrees) in graph streams isfundamental for many applications. For example in a bipartite graphrepresenting user-website visiting activities, user cardinalities (the numberof distinct visited websites) are monitored to report network anomalies. Thesereal-world graph streams may contain user-item duplicates and have a hugenumber of distinct user-item pairs, therefore, it is infeasible to exactlycompute user cardinalities when memory and computation resources arelimited.Existing methods are designed to approximately estimate usercardinalities, whose accuracy highly depends on parameters that are not easy toset. Moreover, these methods cannot provide anytime-available estimation, asthe user cardinalities are computed at the end of the data stream. Real-timeapplications such as anomaly detection require that user cardinalities areestimated on the fly. To address these problems, we develop novel bit andregister sharing algorithms, which use a bit array and a register array tobuild a compact sketch of all users' connected items respectively. Comparedwith previous bit and register sharing methods, our algorithms exploit thedynamic properties of the bit and register arrays (e.g., the fraction of zerobits in the bit array at each time) to significantly improve the estimationaccuracy, and have low time complexity (O(1)) to update the estimations eachtime they observe a new user-item pair. In addition, our algorithms are simpleand easy to use, without requirements to tune any parameter. We evaluate theperformance of our methods on real-world datasets. The experimental resultsdemonstrate that our methods are several times more accurate and faster thanstate-of-the-art methods using the same amount of memory.

Utilizing Dynamic Properties of Sharing Bits and Registers to Estimate User Cardinalities over Time