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Answering reachability and K-reach queries on large graphs with label constraints

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Abstract

The purpose of this paper is to examine the problem of label-constrained reachability (LCR) and K-reach (LCKR) queries, which are fundamental in a wide variety of applications using directed edge-labeled graphs. While reachability and K-reach queries have been extensively researched, LCR and LCKR queries are much more challenging due to the fact that the number of potential label-constraint sets is exponential to the size of the labels. We note that existing techniques for LCR queries only build a partial index and that their worse-case query time could be comparable to that of an online breadth-first search (BFS). This paper proposes a new label-constrained 2-hop indexing method with innovative pruning rules and order strategies. Our work demonstrates that the worst query time could be bounded by the number of in-out index entries. Extensive experiments demonstrate that the proposed methods substantially outperform the state-of-the-art approach in terms of the query response time (up to 5 orders of magnitude speedup), index size, and the index construction time. More precisely, the method we present can response LCR queries across billion-scale networks within microseconds on a single machine. We formally define the problem of LCKR queries and discuss critical applications for addressing it. To tackle the difficulties presented by label and hop constraints, an efficient upper and lower bound is suggested based on a search method. Using all of these techniques, extensive experiments on synthetic and real-world networks demonstrate that our algorithm outperforms the baseline by about three to four orders of magnitude while maintaining competitive indexing time and size.

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Notes

  1. Otherwise, the system will be overwhelmed by false alarms raised by the above path analysis.

  2. To avoid possible ambiguity of “labeling index” and “label-constrained”, we use “2-hop index technique” to present the “2-hop labeling index technique” used in the literature.

  3. Our index construction process for each vertex will return a minimal label path tree.

  4. This is the default setting for LI+ in [41].

  5. Find the minimum distance between \(v_k\) and u in the index \(L_{k-1}\) with label constraints P[u].labels.

  6. w is set due to the initial experiments.

  7. P2H+ uses degree order which is the same as LI+ for the sake of comparison fairness. The effect of vertex order will be compared in Table 8

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Acknowledgements

Xuemin Lin is supported by ARC DP180103096 and DP200101338. Ying Zhang is supported by ARC FT170100128 and ARC DP210101393. Wenjie Zhang is supported by ARC DP200101116 and DP1801003096. Lu Qin is supported by ARC FT200100787 and DP210101347.

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Authors and Affiliations

  1. University of New South Wales, Kensington, Australia

    You Peng, Xuemin Lin & Wenjie Zhang

  2. Centre for AI, University of Technology Sydney, Sydney, Australia

    Ying Zhang & Lu Qin

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  1. You Peng
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Correspondence to You Peng.

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Peng, Y., Lin, X., Zhang, Y. et al. Answering reachability and K-reach queries on large graphs with label constraints. The VLDB Journal 31, 101–127 (2022). https://doi.org/10.1007/s00778-021-00695-0

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