Pay-as-you-go maintenance of precomputed nearest neighbors in large graphs

Abstract

An important building block of many graph applications such as searching in social networks, keyword search in graphs, and retrieval of linked documents is retrieving the transitive neighbors of a node in ascending order of their distances. Since large graphs cannot be kept in memory and graph traversals at query time would be prohibitively expensive, the list of neighbors for each node is usually precomputed and stored in a compact form. While the problem of precomputing all-pairs shortest distances has been well studied for decades, efficiently maintaining this information when the graph changes is not as well understood. This paper presents an algorithm for maintaining nearest neighbor lists in weighted graphs under node insertions and decreasing edge weights. It considers the important case where queries are a lot more frequent than updates, and presents two approaches for transparently performing necessary index updates while executing queries. Extensive experiments with large graphs, including a subset of Twitter's user graph, demonstrate that the overhead for this maintenance is small.