Quick Detection of Top-k Personalized PageRank Lists

Abstract

Abstract. We study a problem of quick detection of top-k Personalized PageRank (PPR) lists. This problem has a number of important applications such as finding local cuts in large graphs, estimation of similarity distance and person name disambiguation. We argue that two observations are important when finding top-k PPR lists. Firstly, it is crucial that we detect fast the top-k most important neighbors of a node, while the exact order in the top-k list and the exact values of PPR are by far not so crucial. Secondly, by allowing a small number of "wrong" elements in top-k lists, we achieve great computational savings, in fact, without degrading the quality of the results. Based on these ideas, we propose Monte Carlo methods for quick detection of top-k PPR lists. We demonstrate the effectiveness of these methods on the Web and Wikipedia graphs, provide performance evaluation and supply stopping criteria.

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.…”

“…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.…”

“…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.…”

Reverse top-k search using random walk with restart

“…The number n = |V | (m = |E|) of nodes (edges) of each graph are shown in Table 2. Web-stanford-cs 3 and Web-stanford 4 were crawled from stanford.edu. Each node is a web domain and a directed link stands for a hyperlink between two nodes.…”

“…The top-k RWR proximity query retrieves the k nodes with the highest proximity from a given query node q in a graph. This problem has been investigated previously and efficient solutions have been proposed for it (e.g., [11,3,10]). …”