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Decentralized Graph Processing for Reachability Queries

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Advanced Data Mining and Applications (ADMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13725))

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Abstract

Answering queries on large graphs is an essential part of data processing. In this paper, we focus on determining reachability between vertices. We propose a labeling scheme which is inherently distributed and can be processed in parallel. We study what properties make it difficult to find a good reachability labeling scheme for directed graphs. We focus on the genus of a graph. For graphs of bounded genus g, we design a labeling scheme of length \(\mathcal {O}(g\log n + {\log }^{2}{n})\). We also prove that no labeling schemes with labels shorter than \(\varOmega (\sqrt{g})\) exist for this graph class.

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References

  1. Abraham, I., Gavoille, C.: Object location using path separators. In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Principles of Distributed Computing, PODC 2006, pp. 188–197. Association for Computing Machinery, New York (2006). https://doi.org/10.1145/1146381.1146411

  2. Adjiashvili, D., Rotbart, N.: Labeling schemes for bounded degree graphs. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8573, pp. 375–386. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43951-7_32

    Chapter  Google Scholar 

  3. Agrawal, R., Borgida, A., Jagadish, H.V.: Efficient management of transitive relationships in large data and knowledge bases. In: Proceedings of the 1989 ACM SIGMOD International Conference on Management of Data, SIGMOD 1989, pp. 253–262. Association for Computing Machinery, New York (1989). https://doi.org/10.1145/67544.66950

  4. Alstrup, S., Bille, P., Rauhe, T.: Labeling schemes for small distances in trees. SIAM J. Discrete Math. 19(2), 448–462 (2005). https://doi.org/10.1137/S0895480103433409

  5. Alstrup, S., Gavoille, C., Kaplan, H., Rauhe, T.: Nearest common ancestors: a survey and a new algorithm for a distributed environment. Theor Comput. Syst. 37(3), 441–456 (2004). https://doi.org/10.1007/s00224-004-1155-5

  6. Alstrup, S., Kaplan, H., Thorup, M., Zwick, U.: Adjacency labeling schemes and induced-universal graphs. In: Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing, STOC 2015, pp. 625–634. Association for Computing Machinery, New York (2015). https://doi.org/10.1145/2746539.2746545

  7. Alstrup, S., Rauhe, T.: Improved labeling scheme for ancestor queries. In: Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002, pp. 947–953. Society for Industrial and Applied Mathematics, USA (2002)

    Google Scholar 

  8. Bonamy, M., Esperet, L., Groenland, C., Scott, A.: Optimal labelling schemes for adjacency, comparability, and reachability, p. 1109–1117. Association for Computing Machinery, New York (2021). https://doi.org/10.1145/3406325.3451102

  9. Breuer, M.: Coding the vertexes of a graph. IEEE Trans. Inf. Theory 12, 148–153 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cheng, J., Huang, S., Wu, H., Fu, A.W.C.: TF-label: a topological-folding labeling scheme for reachability querying in a large graph. In: Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data, SIGMOD 2013, pp. 193–204. Association for Computing Machinery, New York (2013). https://doi.org/10.1145/2463676.2465286

  11. Cohen, E., Halperin, E., Kaplan, H., Zwick, U.: Reachability and distance queries via 2-hop labels. SIAM J. Comput. 32(5), 1338–1355 (2003). https://doi.org/10.1137/S0097539702403098

  12. da Silva, R.F., Urrutia, S., Hvattum, L.M.: Extended high dimensional indexing approach for reachability queries on very large graphs. Exp. Syst. Appl. 181, 114962 (2021). https://doi.org/10.1016/j.eswa.2021.114962. https://www.sciencedirect.com/science/article/pii/S0957417421004036

  13. Dahlgaard, S., Knudsen, M.B.T., Rotbart, N.: A simple and optimal ancestry labeling scheme for trees. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 564–574. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47666-6_45

    Chapter  MATH  Google Scholar 

  14. Eppstein, D.: Dynamic generators of topologically embedded graphs. CoRR cs.DS/0207082 (2002). https://arxiv.org/abs/cs/0207082

  15. Fraigniaud, P., Korman, A.: An optimal ancestry labeling scheme with applications to xml trees and universal posets. J. ACM 63(1) (2016). https://doi.org/10.1145/2794076

  16. Gavoille, C., Peleg, D., Pérennes, S., Raz, R.: Distance labeling in graphs. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2001, pp. 210–219. Society for Industrial and Applied Mathematics, USA (2001)

    Google Scholar 

  17. Gilbert, J.R., Hutchinson, J.P., Tarjan, R.E.: A separator theorem for graphs of bounded genus. J. Algorithms 5(3), 391–407 (1984). https://doi.org/10.1016/0196-6774(84)90019-1. https://www.sciencedirect.com/science/article/pii/0196677484900191

  18. Heinis, T., Alonso, G.: Efficient lineage tracking for scientific workflows. In: Proceedings of the 2008 ACM SIGMOD International Conference on Management of Data, SIGMOD 2008, pp. 1007–1018. Association for Computing Machinery, New York (2008). https://doi.org/10.1145/1376616.1376716

  19. Jain, R., Tewari, R.: Reachability in high treewidth graphs. In: Lu, P., Zhang, G. (eds.) 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), vol. 149, pp. 12:1–12:14. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2019). https://doi.org/10.4230/LIPIcs.ISAAC.2019.12. https://drops.dagstuhl.de/opus/volltexte/2019/11508

  20. Kannan, S., Naor, M., Rudich, S.: Implicit representation of graphs. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 334–343. Association for Computing Machinery, New York (1988). https://doi.org/10.1145/62212.62244

  21. Kawarabayashi, K., Klein, P.N., Sommer, C.: Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6755, pp. 135–146. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22006-7_12

    Chapter  MATH  Google Scholar 

  22. Liu, Y.: Topological theory of graphs: de Gruyter (2017). https://doi.org/10.1515/9783110479492

  23. Peleg, D.: Informative labeling schemes for graphs. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 579–588. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44612-5_53

    Chapter  Google Scholar 

  24. Seufert, S., Anand, A., Bedathur, S., Weikum, G.: FERRARI: flexible and efficient reachability range assignment for graph indexing. In: 2013 IEEE 29th International Conference on Data Engineering (ICDE), pp. 1009–1020 (2013). https://doi.org/10.1109/ICDE.2013.6544893

  25. Simon, K.: An improved algorithm for transitive closure on acyclic digraphs. In: Kott, L. (ed.) ICALP 1986. LNCS, vol. 226, pp. 376–386. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-16761-7_87

    Chapter  Google Scholar 

  26. Thomassen, C.: Kuratowski’s theorem. J. Graph Theor. 5(3), 225–241 (1981). https://doi.org/10.1002/jgt.3190050304. https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.3190050304

  27. Thorup, M.: Compact oracles for reachability and approximate distances in planar digraphs. J. ACM 51(6), 993–1024 (2004). https://doi.org/10.1145/1039488.1039493

  28. Wang, H., He, H., Yang, J., Yu, P., Yu, J.: Dual labeling: answering graph reachability queries in constant time. In: 22nd International Conference on Data Engineering (ICDE 2006), pp. 75–75 (2006). https://doi.org/10.1109/ICDE.2006.53

  29. Wei, H., Yu, J.X., Lu, C., Jin, R.: Reachability querying: an independent permutation labeling approach. VLDB J. 27(1), 1–26 (2017). https://doi.org/10.1007/s00778-017-0468-3

    Article  Google Scholar 

  30. Yildirim, H., Chaoji, V., Zaki, M.J.: GRAIL: scalable reachability index for large graphs. Proc. VLDB Endow. 3(1–2), 276–284 (2010). https://doi.org/10.14778/1920841.1920879

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Authors and Affiliations

  1. ETH Zürich, Zürich, Switzerland

    Joël Mathys, Robin Fritsch & Roger Wattenhofer

Authors
  1. Joël Mathys
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  2. Robin Fritsch
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  3. Roger Wattenhofer
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Corresponding author

Correspondence to Joël Mathys .

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Editors and Affiliations

  1. The University of Adelaide, Adelaide, SA, Australia

    Weitong Chen

  2. The University of New South Wales, Sydney, NSW, Australia

    Lina Yao

  3. Macquarie University, Sydney, NSW, Australia

    Taotao Cai

  4. Griffith University, Brisbane, QLD, Australia

    Shirui Pan

  5. Microsoft, Beijing, China

    Tao Shen

  6. The University of Queensland, Brisbane, QLD, Australia

    Xue Li

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Mathys, J., Fritsch, R., Wattenhofer, R. (2022). Decentralized Graph Processing for Reachability Queries. In: Chen, W., Yao, L., Cai, T., Pan, S., Shen, T., Li, X. (eds) Advanced Data Mining and Applications. ADMA 2022. Lecture Notes in Computer Science(), vol 13725. Springer, Cham. https://doi.org/10.1007/978-3-031-22064-7_36

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  • DOI: https://doi.org/10.1007/978-3-031-22064-7_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22063-0

  • Online ISBN: 978-3-031-22064-7

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