HyperHeadTail: a Streaming Algorithm for Estimating the Degree Distribution of Dynamic Multigraphs

Abstract

We introduce HyperHeadTail, a streaming algorithm for estimating the degree distribution of a graph from a stream of edges using very little storage space. Real world graph streams, such as those generated by network traffic or other communication networks, tend to contain repeated elements as well as a temporal nature. Our algorithm handles these situations by extending the HeadTail algorithm of Simpson, Seshadhri, and McGregor [20]. We provide an implementation of HyperHeadTail and demonstrate its utility on both synthetic and real-world data sets. We show that HyperHeadTail offers similar performance to HeadTail, while also providing additional functionality for tracking dynamic graphs that previous algorithms cannot efficiently achieve. We show that with a space usage on the order of 8% of the number of vertices in a graph, we were able to achieve a Relative Hausdorff distance of .27.