Unbiasedly Estimate Temporal Katz Centrality and Identify Top-K Vertices in Streaming Graph

In the realm of network, finding top-K influential vertices in data streams is a fundamental problem. Among these, Katz centrality serves as a valuable metric in the analysis of graph. Nevertheless, the computation of Katz centrality demands substantial resources. Therefore, this paper introduces an innovative approach to estimate top-K temporal Katz centrality. To achieve this, we propose a data structure called TAS-PFAH. It consists of a filter and a Count Sketch. The Count Sketch employs the tug-of-war principle to provide an unbiased estimation of vertices. Concurrently, the filter serves as a repository for the vertices, dynamically maintaining the foremost K vertices in temporal graph. It is implemented by a min-heap structure accelerated by an auxiliary hash table to ensure O(1) lookup time cost. The introduction of filter not only enhances the rate of enquiring vertex which has high temporal Katz centrality, but also reduces the noise of other vertices which recorded in the Count Sketch. Because the combination of filter and sketch, our algorithm achieves high accuracy with limited memory.