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Efficient processing of \(k\)-hop reachability queries

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Abstract

We study the problem of answering k -hop reachability queries in a directed graph, i.e., whether there exists a directed path of length \(k\), from a source query vertex to a target query vertex in the input graph. The problem of \(k\)-hop reachability is a general problem of the classic reachability (where \(k=\infty \)). Existing indexes for processing classic reachability queries, as well as for processing shortest path distance queries, are not applicable or not efficient for processing \(k\)-hop reachability queries. We propose an efficient index for processing \(k\)-hop reachability queries. Our experimental results on a wide range of real datasets show that our method is efficient and scalable in terms of both index construction and query processing.

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Notes

  1. Note that 3-hop is only the name of the index [27] for processing classic reachability queries, and does not imply 3-hop reachability.

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Acknowledgments

The authors would like to thank the reviewers for their constructive comments. This research is supported in part by CUHK direct grant 4055017, and grants from the Research Grants Council of the Hong Kong SAR (CUHK 411211 and CUHK 418512).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, New Territories, Hong Kong

    James Cheng

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, New Territories, Hong Kong

    Zechao Shang, Hong Cheng & Jeffrey Xu Yu

  3. Microsoft Research Asia, Beijing, China

    Haixun Wang

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  1. James Cheng
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  2. Zechao Shang
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  3. Hong Cheng
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  4. Haixun Wang
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  5. Jeffrey Xu Yu
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Corresponding author

Correspondence to James Cheng.

Appendix

Appendix

Algorithm 6 presents an extension of Algorithm 4 to return the exact shortest path distance from \(s\) to \(t\) if \(s\) can reach \(t\) in \(k\) hops. The main difference is that in Algorithm 4, we can terminate the process as soon as we find that \(s\) can reach \(t\) in \(k\) hops in \(D_1\) or \(D_2\) or \(D_3\), while in Algorithm 6 we need to continue with the intersection and join in order to find the minimum distance. However, the complexity of Algorithm 6 is the same as that of Algorithm 4 given in Sect. 5.5, since we give the worst case complexity in Sect. 5.5.

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Cheng, J., Shang, Z., Cheng, H. et al. Efficient processing of \(k\)-hop reachability queries. The VLDB Journal 23, 227–252 (2014). https://doi.org/10.1007/s00778-013-0346-6

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