IRWR: incremental random walk with restart

Random Walk with Restart (RWR) has become an appealing measure of node proximities in emerging applications \eg recommender systems and automatic image captioning. In practice, a real graph is typically large, and is frequently updated with small changes. It is often cost-inhibitive to recompute proximities from scratch via \emph{batch} algorithms when the graph is updated. This paper focuses on the incremental computations of RWR in a dynamic graph, whose edges often change over time. The prior attempt of RWR [1] deploys \kdash to find top-$k$ highest proximity nodes for a given query, which involves a strategy to incrementally \emph{estimate} upper proximity bounds. However, due to its aim to prune needless calculation, such an incremental strategy is \emph{approximate}: in $O(1)$ time for each node. The main contribution of this paper is to devise an \emph{exact} and fast incremental algorithm of RWR for edge updates. Our solution, \IRWR\!, can incrementally compute any node proximity in $O(1)$ time for each edge update without loss of exactness. The empirical evaluations show the high efficiency and exactness of \IRWR for computing proximities on dynamic networks against its batch counterparts.