Atlas: Approximating Shortest Paths in Social Graphs

The search for shortest paths is an essential primitive for a variety of graph-based applications, particularly those on online so cial networks. For example, LinkedIn users perform queries to find the shortest pa th “social links” connecting them to a particular user to facilitate introduc tions. This type of graph query is challenging for moderately sized graphs, but becom s computationally intractable for graphs underlying today’s social networks , most of which contain millions of nodes and billions of edges. We propose Atlas, a novel approach to scalably approximate shortest paths between graph nodes us ing a collection of spanning trees. Spanning trees are easy to generate, compac t relative to original graphs, and can be distributed across machines to paralleli ze queries. We demonstrate its scalability and effectiveness using 6 large soci al graphs from Facebook, Orkut and Renren, the largest of which includes 43 million no des and 1 billion edges. We describe techniques to incrementally update Atla s as social graphs change over time. We capture graph dynamics using 35 daily sn apshots of a Facebook network, and show that Atlas can amortize the cost of tre e updates over time. Finally, we apply Atlas to several graph applications, and s how that they produce results that closely approximate ideal results.