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Efficient structure similarity searches: a partition-based approach

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Abstract

Graphs are widely used to model complex data in many applications, such as bioinformatics, chemistry, social networks, pattern recognition. A fundamental and critical query primitive is to efficiently search similar structures in a large collection of graphs. This article mainly studies threshold-based graph similarity search with edit distance constraints. Existing solutions to the problem utilize fixed-size overlapping substructures to generate candidates, and thus become susceptible to large vertex degrees and distance thresholds. In this article, we present a partition-based approach to tackle the problem. By dividing data graphs into variable-size non-overlapping partitions, the edit distance constraint is converted to a graph containment constraint for candidate generation. We develop efficient query processing algorithms based on the novel paradigm. Moreover, candidate-pruning techniques and an improved graph edit distance verification algorithm are developed to boost the performance. In addition, a cost-aware graph partitioning method is devised to optimize the index. Extending the partition-based filtering paradigm, we present a solution to the top-\(k\) graph similarity search problem, where tailored filtering, look-ahead and computation-sharing strategies are exploited. Using both public real-life and synthetic datasets, extensive experiments demonstrate that our approaches significantly outperform the baseline and its alternatives.

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Notes

  1. An elaborated discussion is provided in Part A of supplementary material to this article.

  2. A partition can be either connected or disconnected.

  3. For example, a partition contained by the query for Pars, or a \(q\)-gram appearing in the query’s \(q\)-gram multiset for \(\kappa \)-AT.

  4. The special case of \(\tau = 1\) is polynomially reducible from the partition problem that decides whether a given multiset of numbers can be partitioned into two subsets such that the sums of elements in both subsets are equal, and thus, is NP-hard.

  5. http://dtp.nci.nih.gov/docs/aids/aids_data.html.

  6. http://www.iam.unibe.ch/fki/databases/iam-graph-database/download-the-iam-graph-database.

  7. http://www.cs.washington.edu/research/xmldatasets/.

  8. http://www.cse.ust.hk/graphgen/.

  9. This RAM configuration is to accommodate the A \(^*\)-based verification algorithm, which needs to maintain a large number of partial mappings in a priority queue.

  10. Some of the experiments were manually terminated after running for 24 h, the duration of which was reported instead.

  11. Onwards this method is adopted for summarizing experiment results if not otherwise specified, and figures of the same results in logarithmic scale can be found in Part C of supplementary material to this article.

  12. The original algorithm does not come with exact verification [7].

  13. There is a pile of literature dedicated to subgraph similarity search based on MCS, e.g., [12, 19, 26].

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Acknowledgements

Funding was provided by Japan Society for the Promotion of Science (Grant No. 16H01722), National Natural Science Foundation of China (Grant Nos. 61402494, 71690233), Natural Science Foundation of Hunan Province (Grant No. 2015JJ4009) and Australian Research Council (Grant Nos. DP150103071 and DP150102728).

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Authors and Affiliations

  1. National University of Defense Technology, Changsha, China

    Xiang Zhao

  2. Collaborative Innovation Center of Geospatial Technology, Wuhan, China

    Xiang Zhao

  3. Nagoya University, Nagoya, Japan

    Chuan Xiao

  4. The University of New South Wales, Sydney, Australia

    Xuemin Lin, Wenjie Zhang & Yang Wang

Authors
  1. Xiang Zhao
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  2. Chuan Xiao
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  3. Xuemin Lin
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  4. Wenjie Zhang
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  5. Yang Wang
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Correspondence to Chuan Xiao.

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Zhao, X., Xiao, C., Lin, X. et al. Efficient structure similarity searches: a partition-based approach. The VLDB Journal 27, 53–78 (2018). https://doi.org/10.1007/s00778-017-0487-0

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