Fast Nearest Neighbor Search on Large Time-Evolving Graphs.

Finding the k nearest neighbors (k-nns) of a given vertex in a graph has many applications such as link prediction, keyword search, and image tagging. An established measure of vertex-proximity in graphs is the Personalized Page Rank (ppr) score based on random walk with restarts. Since ppr scores have long-range correlations, computing them accurately and efficiently is challenging when the graph is too large to fit in main memory, especially when it also changes over time. In this work, we propose an efficient algorithm to answer ppr-based k-nn queries in large time-evolving graphs. Our key approach is to use a divide-and-conquer framework and efficiently compute answers in a distributed fashion. We represent a given graph as a collection of dense vertex-clusters with their inter connections. Each vertex-cluster maintains certain information related to internal random walks and updates this information as the graph changes. At query time, we combine this information from a small set of relevant clusters and compute ppr scores efficiently. We validate the effectiveness of our method on large real-world graphs from diverse domains. To the best of our knowledge, this is one of the few works that simultaneously addresses answering k-nn queries in possibly disk-resident and time-evolving graphs.