Fast and exact top-k search for random walk with restart

Abstract

Graphs are fundamental data structures and have been employed for centuries to model real-world systems and phenomena. Random walk with restart (RWR) provides a good proximity score between two nodes in a graph, and it has been successfully used in many applications such as automatic image captioning, recommender systems, and link prediction. The goal of this work is to find nodes that have topk highest proximities for a given node. Previous approaches to this problem find nodes efficiently at the expense of exactness. The main motivation of this paper is to answer, in the affirmative, the question, 'Is it possible to improve the search time without sacrificing the exactness?'. Our solution, Kdash, is based on two ideas: (1) It computes the proximity of a selected node efficiently by sparse matrices, and (2) It skips unnecessary proximity computations when searching for the top-k nodes. Theoretical analyses show that K-dash guarantees result exactness. We perform comprehensive experiments to verify the efficiency of K-dash. The results show that K-dash can find top-k nodes significantly faster than the previous approaches while it guarantees exactness.

Reducing seed noise in personalized PageRank

“…Moreover, we also show that -these can be obtained highly efficiently, if necessary, leveraging existing approximation algorithms [2,4,14,17,21,23,41] and/or parallel implementations [3,32] for computing the PPR scores, -the proposed formulations are reuse-promoting in the sense that, it is possible to divide the work relative to individual seed nodes and cache the intermediary results obtained during the computation -these cached results can then be reused for future queries sharing seed nodes, and -especially in systems with large query throughputs, it may be possible to cluster queries based on the partial overlaps between the seed sets and, thus, significantly reduce the overall robust PPR computation costs.…”

“…Alternatively, PowerIteration [27] or using iterative approximations [14,30], which explicitly simulate the dissemination of probability mass by repeatedly applying the transition process to an initial distribution π 0 until a convergence criterion is satisfied. Recent advances on PPR computation include top-k and approximate personalized PageRank algorithms [2,4,14,17,21,23,41] and parallelized implementations on MapReduce or Pregel based systems [3,32,36,38]. The FastRWR algorithm [41], for example partitions the graph into subgraphs and indexes partial intermediary solutions.…”

“…This is especially advantageous when G is large as we can leverage any of the highly effective approximation algorithms [2,4,14,17,21,23,41] or parallelized implementations [3,32] for computing these PPR scores. Most importantly, the first step of the algorithm (where we solve a linear equation independently for each seed node) can be trivially parallelized by assigning each node to a different computation unit.…”

Efficient Processing Node Proximity via Random Walk with Restart

“…RWR is a PageRank-like node proximity based on a random surfer model. In comparison with other relevance measures, RWR has the following two benefits [5]: (1) it can globally capture the entire topology of a graph; (2) its proximity values can be used for ranking objects with respects to a certain query, as opposed to PageRank that is query-independent.…”

“…Very recently, for top-K search, Fujiwara et al [1] has proposed an excellent algorithm called k-dash, which can be regarded as the state-of-the-art one for computing RWR. Unfortunately, their strategy involves a large LU matrix decomposition over an entire graph, which is still time-consuming.…”