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Graph similarity search on large uncertain graph databases

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Abstract

Many studies have been conducted on seeking an efficient solution for graph similarity search over certain (deterministic) graphs due to its wide application in many fields, including bioinformatics, social network analysis, and Resource Description Framework data management. All prior work assumes that the underlying data is deterministic. However, in reality, graphs are often noisy and uncertain due to various factors, such as errors in data extraction, inconsistencies in data integration, and for privacy-preserving purposes. Therefore, in this paper, we study similarity graph containment search on large uncertain graph databases. Similarity graph containment search consists of subgraph similarity search and supergraph similarity search. Different from previous works assuming that edges in an uncertain graph are independent of each other, we study uncertain graphs where edges’ occurrences are correlated. We formally prove that subgraph or supergraph similarity search over uncertain graphs is \(\#\)P-hard; thus, we employ a filter-and-verify framework to speed up these two queries. For the subgraph similarity query, in the filtering phase, we develop tight lower and upper bounds of subgraph similarity probability based on a probabilistic matrix index (PMI). PMI is composed of discriminative subgraph features associated with tight lower and upper bounds of subgraph isomorphism probability. Based on PMI, we can filter out a large number of uncertain graphs and maximize the pruning capability. During the verification phase, we develop an efficient sampling algorithm to validate the remaining candidates. For the supergraph similarity query, in the filtering phase, we propose two pruning algorithms, one lightweight and the other strong, based on maximal common subgraphs of query graph and data graph. We run the two pruning algorithms against a probabilistic index that consists of powerful graph features. In the verification, we design an approximate algorithm based on the Horvitz–Thompson estimator to fast validate the remaining candidates. The efficiencies of our proposed solutions to the subgraph and supergraph similarity search have been verified through extensive experiments on real uncertain graph datasets.

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Notes

  1. Neighbor edges are the edges that are incident to the same vertex or the edges of a triangle.

  2. In this paper, we consider undirected graphs, although it is straightforward to extend our methods to directed graphs.

  3. Without loss of the generality, in this paper, we assume a query graph is a connected deterministic graph, and an uncertain graph is connected.

  4. According to the subgraph similarity search, insertion does not change the query graph.

  5. For \(g\in SC_{q}\), we have \( d\le \delta \), since the uncertain graphs with \(d>\delta \) have been filtered out in the structural pruning.

  6. In this paper, we use the algorithm in [47] to compute embeddings of a feature in \(g^c\).

  7. We only show the relaxed queries containing features in graph \(001^c\).

  8. http://string-db.org.

  9. http://thebiogrid.org.

  10. http://www.ncbi.nih.gov/COG.

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Acknowledgments

Ye Yuan is supported by the NSFC (Grant No. 61100024) and the Fundamental Research Funds for the Central Universities (Grant No. N130504006). Guoren Wang is supported by the NSFC (Grant No. 61025007, 61328202 and U1401256), National Basic Research Program of China (973, Grant No. 2011CB302200-G), National High Technology Research and Development 863 Program of China (Grant No. 2012AA011004). Lei Chen is supported by the NSFC (Grant No. 61328202), the Hong Kong RGC Project N HKUST637/13, National Grand Fundamental Research 973 Program of China under Grant 2014CB340300, Microsoft Research Asia Gift Grant and Google Faculty Award 2013.

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Authors and Affiliations

  1. Northeastern University, Shenyang, China

    Ye Yuan & Guoren Wang

  2. Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong

    Lei Chen

  3. Google, Mountain View, CA, USA

    Haixun Wang

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  1. Ye Yuan
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Correspondence to Ye Yuan.

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Yuan, Y., Wang, G., Chen, L. et al. Graph similarity search on large uncertain graph databases. The VLDB Journal 24, 271–296 (2015). https://doi.org/10.1007/s00778-014-0373-y

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