Graph Stream Sketch: Summarizing Graph Streams With High Speed and Accuracy
Xiangyang Gou, Lei Zou, Chenxingyu Zhao, Tong Yang
Abstract
A graph stream is a continuous sequence of data items, in which each item indicates an edge, including its two endpoints and edge weight. It forms a dynamic graph that changes with every item. Graph streams play important roles in cyber security, social networks, cloud troubleshooting systems and more. Due to the vast volume and high update speed of graph streams, traditional data structures for graph storage such as the adjacency matrix and the adjacency list are no longer sufficient. However, prior art of graph stream summarization either supports limited kinds of queries or suffers from poor accuracy of query results. In this paper, we propose a novel <i>G</i> raph <i>S</i> tream <i>S</i> ketch (GSS for short) to summarize the graph streams, which has linear space cost <inline-formula><tex-math notation="LaTeX">$O(|E|)$</tex-math></inline-formula> (E is the edge set of the graph) and high update speed, and supports most kinds of queries over graph streams with controllable errors. Experimental results show that our solution is up to 142 times faster than the adjacency list when processing updates in graph streams, and its memory consumption is as small as <inline-formula><tex-math notation="LaTeX">$30\%$</tex-math></inline-formula> of the adjacency list. Though error is introduced as a trade off in our solution, both theoretical analysis and experiment results confirm that such error is small and controllable. The relative error is below <inline-formula><tex-math notation="LaTeX">$10^{-2}$</tex-math></inline-formula> in edge weight query, and the precision is above <inline-formula><tex-math notation="LaTeX">$90\%$</tex-math></inline-formula> is 1-hop precursor/successor queries.