Identifying Converging Pairs of Nodes on a Budget.

In this paper, we consider large graphs that evolve over time, such as graphs that model social networks. Given two instances of the graph at two points in time, we ask to identify the top pairs of nodes whose shortest path distance has decreased the most. We call these pairs converging. The straightforward way to address this problem is by computing the shortest path distances of all pairs at both instances and keeping the ones with the largest di↵erences. Since for large networks this is computationally infeasible, we consider a budgeted version of the problem, where given a fixed budget of single-source shortest path computations, we seek to identify nodes that participate in as many converging pairs as possible. We evaluate a number of di↵erent approaches for our problem, that employ centrality-based, dispersion-based, and landmark-based distance estimation metrics. We also consider a classification-based approach that builds a classifier that combines the above features for predicting whether a node participates in one of the top converging pairs. We present experimental results using realworld datasets that show that we are able to identify the large majority of the top converging pairs on a very small budget.