Indexing Public-Private Graphs

We consider the reachability indexing problem for privatepublic directed graphs. In these graphs nodes come in three flavors: public—nodes visible to all users, private—nodes visible to a specific set of users, and protected—nodes visible to any user who can see at least one of the node’s parents. We are interested in computing the set of nodes visible to a specific user online. There are two obvious algorithms: precompute the result for every user, or run a reachability algorithm at query time. This paper explores the trade-off between these two strategies. Our approach is to identify a set of additional visible seed nodes for each user. The online reachability algorithm explores the graph starting at these nodes. We first formulate the problem as asymmetric k-center with outliers, and then give an efficient and practical algorithm. We prove new theoretical guarantees for this problem and show empirically that it performs very well in practice.