An efficient similarity search framework for SimRank over large dynamic graphs

Abstract

SimRank is an important measure of vertex-pair similarity according to the structure of graphs. The similarity search based on Sim-Rank is an important operation for identifying similar vertices in a graph and has been employed in many data analysis applications. Nowadays, graphs in the real world become much larger and more dynamic. The existing solutions for similarity search are expensive in terms of time and space cost. None of them can efficiently support similarity search over large dynamic graphs. In this paper, we propose a novel two-stage random-walk sampling framework (TSF) for SimRank-based similarity search (e.g., top-k search). In the preprocessing stage, TSF samples a set of one-way graphs to index raw random walks in a novel manner within O(N Rg) time and space, where N is the number of vertices and Rg is the number of one-way graphs. The one-way graph can be efficiently updated in accordance with the graph modification, thus TSF is well suited to dynamic graphs. During the query stage, TSF can search similar vertices fast by naturally pruning unqualified vertices based on the connectivity of one-way graphs. Furthermore, with additional Rq samples, TSF can estimate the SimRank score with probability 1 − 2e −2ǫ 2 Rg Rq (1−c) 2 if the error of approximation is bounded by 1 − ǫ. Finally, to guarantee the scalability of TSF, the one-way graphs can also be compactly stored on the disk when the memory is limited. Extensive experiments have demonstrated that TSF can handle dynamic billion-edge graphs with high performance.

C-Rank: A link-based similarity measure for scientific literature databases

“…Third, although the semantics in the direction of links is lost, it is advantageous to disregard the direction of links in similarity computation. Finally, since the computation of C-Rank is fundamentally the same as that of SimRank, except that C-Rank disregards the direction of links, many of the methods [8,9,14,22,35,43,45,49,50] to improve the time complexity of SimRank can be applied to C-Rank.…”

“…However, the worst-case time complexity of all existing iterative measures including C-Rank is O(n 4 ). Many methods have been proposed to improve the time complexity of SimRank [8,9,14,22,35,43,45,49,50]. These methods can be applied to C-Rank because the computation of C-Rank is fundamentally the same as that of SimRank except that C-Rank disregards the direction of links.…”

Realtime index-free single source SimRank processing on web-scale graphs

“…READS [12] precomputes √ c-walks and compresses the walks into trees. During query processing, READS retrieves the walks originating from the query node u, and finds all the √ c-walks that meet with the √ c-walks of u. TSF [28] builds an index consisting of one-way graphs by sampling one in-neighbor from each node's in-coming edges. During query processing, the one-way graphs are used to simlulate random walks to estimate SimRank.…”

“…Several recent approaches, notably [12,15,21,28,31,33], have demonstrated promising results for single source Sim-Rank processing, by solving the approximate version of the problem with rigorous result quality guarantees, as elaborated in Section 2. The majority of these methods, however, require extensive pre-processing to index the input graph G; as explained in Section 2.2, such indexes cannot be easily updated when the underlying graph G changes, meaning that these methods are not suitable for our target scenarios described above.…”

“…The majority of these methods, however, require extensive pre-processing to index the input graph G; as explained in Section 2.2, such indexes cannot be easily updated when the underlying graph G changes, meaning that these methods are not suitable for our target scenarios described above. Specifically, the current state of the art for offline single source SimRank is PRSim [33], which achieves [28] O n log n δ / 2 O n log n δ / 2 O n log n δ / 2 READS [12] O n log n δ / 2 O n log n δ / 2 O n log n δ / 2 ProbeSim [21] O n log n δ / 2 --SLING [31] O(n/ ) O(n/ ) O m/ + n log n δ / 2 PRSim [33] 1 O n log n δ / 2 O(min {n/ , m}) O(m/ ) efficient query processing with a relatively lightweight index; nevertheless, it is clearly infeasible to rebuild index for every graph update or new query, as shown in our experiments in Section 5. The current best index-free solution is ProbeSim [33], whose query efficiency is far lower than that of PRSim.…”