Skip to main content

External Topological Sorting in Large Graphs

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10827))

Abstract

Topological sorting is a fundamental problem in graph analysis. Given the fact that real world graphs grow rapidly so that they cannot entirely reside in main memory, in this paper, we study external memory algorithms for the topological sorting problem. We propose a contraction-expansion paradigm and devise an external memory algorithm based on the paradigm for the topological sorting problem. Our new algorithm is efficient due to the introduction of the new paradigm and can be implemented easily by using the fundamental external memory primitives. We conduct extensive experiments on real and synthesis graphs and the results demonstrate the efficiency of our proposed algorithm.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    http://newsroom.fb.com/company-info.

  2. 2.

    http://law.di.unimi.it/datasets.php.

  3. 3.

    http://stxxl.org/.

  4. 4.

    http://chato.cl/webspam/datasets/uk2007/links/.

References

  1. Aggarwal, A., Vitter, J., et al.: The input/output complexity of sorting and related problems. Commun. ACM 31(9), 1116–1127 (1988)

    Article  MathSciNet  Google Scholar 

  2. Ajwani, D., Cosgaya-Lozano, A., Zeh, N.: A topological sorting algorithm for large graphs. J. Exp. Algorithmics 17, Article No. 3.2 (2012)

    Article  MathSciNet  Google Scholar 

  3. Angel, E., Campigotto, R., Laforest, C.: Analysis and comparison of three algorithms for the vertex cover problem on large graphs with low memory capacities. Algorithmic Oper. Res. 6(1), 56–67 (2011)

    MathSciNet  MATH  Google Scholar 

  4. Arge, L., Revsbæk, M.: I/O-efficient contour tree simplification. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 1155–1165. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10631-6_116

    Chapter  Google Scholar 

  5. Buccafurri, F., Lax, G., Nocera, A., Ursino, D.: Moving from social networks to social internetworking scenarios: the crawling perspective. Inf. Sci. 256, 126–137 (2014)

    Article  MathSciNet  Google Scholar 

  6. Cheng, J., Ke, Y., Chu, S., Özsu, M.T.: Efficient core decomposition in massive networks. In: Proceedings of ICDE, pp. 51–62 (2011)

    Google Scholar 

  7. Cheng, J., Ke, Y., Fu, A.W.-C., Yu, J.X., Zhu, L.: Finding maximal cliques in massive networks. TODS 36(4), 21 (2011)

    Article  Google Scholar 

  8. Chiang, Y.-J., Goodrich, M.T., Grove, E.F., Tamassia, R., Vengroff, D.E.: External-memory graph algorithms. In: SODA, vol. 95, pp. 139–149 (1995)

    Google Scholar 

  9. Cormen, T.H.: Introduction to Algorithms. MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  10. Hu, X., Tao, Y., Chung, C.-W.: Massive graph triangulation. In: Proceedings of SIGMOD, pp. 325–336 (2013)

    Google Scholar 

  11. Maheshwari, A., Zeh, N.: I/O-efficient planar separators. SIAM J. Comput. 38(3), 767–801 (2008)

    Article  MathSciNet  Google Scholar 

  12. Raith, A., Ehrgott, M.: A comparison of solution strategies for biobjective shortest path problems. Comput. Oper. Res. 36(4), 1299–1331 (2009)

    Article  MathSciNet  Google Scholar 

  13. Tarjan, R.E.: Edge-disjoint spanning trees and depth-first search. Acta Inform. 6(2), 171–185 (1976)

    Article  MathSciNet  Google Scholar 

  14. Wang, J., Cheng, J.: Truss decomposition in massive networks. Proc. VLDB Endow. 5(9), 812–823 (2012)

    Article  Google Scholar 

  15. Yuan, L., Qin, L., Lin, X., Chang, L., Zhang, W.: Diversified top-k clique search. VLDB J. 25(2), 171–196 (2016)

    Article  Google Scholar 

  16. Yuan, L., Qin, L., Lin, X., Chang, L., Zhang, W.: I/O efficient ECC graph decomposition via graph reduction. PVLDB 9(7), 516–527 (2016)

    Google Scholar 

  17. Yuan, L., Qin, L., Lin, X., Chang, L., Zhang, W.: I/O efficient ECC graph decomposition via graph reduction. VLDB J. 26(2), 275–300 (2017)

    Article  Google Scholar 

  18. Zhang, Z., Yu, J.X., Qin, L., Shang, Z.: Divide & conquer: I/O efficient depth-first search. In: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, pp. 445–458 (2015)

    Google Scholar 

Download references

Acknowledgements

Long Yuan is supported by Huawei YBN2017100007. Fan Zhang is supported by Huawei YBN2017100007. Lu Qin is supported by ARC DP160101513. Xuemin Lin is supported by NSFC 61672235, ARC DP170101628, DP180103096 and Huawei YBN2017100007. Wenjie Zhang is supported by ARC DP180103096 and Huawei YBN2017100007.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Long Yuan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Qing, Z., Yuan, L., Zhang, F., Qin, L., Lin, X., Zhang, W. (2018). External Topological Sorting in Large Graphs. In: Pei, J., Manolopoulos, Y., Sadiq, S., Li, J. (eds) Database Systems for Advanced Applications. DASFAA 2018. Lecture Notes in Computer Science(), vol 10827. Springer, Cham. https://doi.org/10.1007/978-3-319-91452-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91452-7_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91451-0

  • Online ISBN: 978-3-319-91452-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics