Persistent graph stream summarization for real-time graph analytics

In massive and rapid graph streams, a useful and important task is to summarize the structure of graph streams in order to enable efficient and effective graph query processing. Although this task has been extensively studied in the literature, we observe that the existing solutions for graph sketches can only answer queries about the current status of the graph stream. In this paper, we aim at designing persistent graph sketches to support graph queries in any given time range in the past. To this end, we first introduce a baseline method by extending an existing graph summarization method. However, our empirical study suggests that the accuracy performance of the baseline method is unsatisfactory, especially when the query time interval is large. To tackle this issue, we propose a new method PGSS-BDH, which stores the streaming edges using a set of hierarchically organized hashmaps. When a query arrives, we divide the query time interval into a set of disjoint sub-intervals and return the sum of query results on all sub-intervals as the overall query answer. Observing that PGSS-BDH bears a linear space cost to the graph stream size, we further propose an advance method PGSS-MDC by using a set of fixed-size hierarchical counters to store the weight of edges, where the query processing is similar to PGSS-BDH. We theoretically analyze the accuracy performance of PGSS-BDH and PGSS-MDC. The experiment results on real-life datasets demonstrate that PGSS-MDC can return much more accurate answers than the competitors by consuming comparable query time and much less memory.