Skip to main content

Fast Computation of Reachability Labeling for Large Graphs

  • Conference paper
Advances in Database Technology - EDBT 2006 (EDBT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3896))

Included in the following conference series:

Abstract

The need of processing graph reachability queries stems from many applications that manage complex data as graphs. The applications include transportation network, Internet traffic analyzing, Web navigation, semantic web, chemical informatics and bio-informatics systems, and computer vision. A graph reachability query, as one of the primary tasks, is to find whether two given data objects, u and v, are related in any ways in a large and complex dataset. Formally, the query is about to find if v is reachable from u in a directed graph which is large in size. In this paper, we focus ourselves on building a reachability labeling for a large directed graph, in order to process reachability queries efficiently. Such a labeling needs to be minimized in size for the efficiency of answering the queries, and needs to be computed fast for the efficiency of constructing such a labeling. As such a labeling, 2-hop cover was proposed for arbitrary graphs with theoretical bounds on both the construction cost and the size of the resulting labeling. However, in practice, as reported, the construction cost of 2-hop cover is very high even with super power machines. In this paper, we propose a novel geometry-based algorithm which computes high-quality 2-hop cover fast. Our experimental results verify the effectiveness of our techniques over large real and synthetic graph datasets.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Agrawal, R., Borgida, A., Jagadish, H.V.: Efficient management of transitive relationships in large data and knowledge bases. In: Proc. of SIGMOD 1989 (1989)

    Google Scholar 

  2. Cohen, E., Halperin, E., Kaplan, H., Zwick, U.: Reachability and distance queries via 2-hop labels. In: Proc. of SODA 2002 (2002)

    Google Scholar 

  3. Cohen, E., Kaplan, H., Milo, T.: Labeling dynamic XML trees. In: Proc. of PODS 2002 (2002)

    Google Scholar 

  4. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  5. Gallo, G., Grigoriadis, M.D., Tarjan, R.E.: A fast parametric maximum flow algorithm and applications. SIAM J. Comput. 18(1), 30–55 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  6. Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Proc. of SIGMOD 1984 (1984)

    Google Scholar 

  7. Ioannidis, Y.E.: On the computation of the transitive closure of relational operators. In: Proc. of VLDB 1986 (1986)

    Google Scholar 

  8. Johnson, D.S.: Approximation algorithms for combinatorial problems. In: Proc. of STOC 1973 (1973)

    Google Scholar 

  9. Johnsonbaugh, R., Kalin, M.: A graph generation software package. In: Proc. Of SIGCSE 1991 (1991), http://condor.depaul.edu/rjohnson/algorithm

  10. Kameda, K.: On the vector representation of the reachability in planar directed graphs. Information Processing Letters 3(3) (1975)

    Google Scholar 

  11. Kaplan, H., Milo, T., Shabo, R.: A comparison of labeling schemes for ancestor queries. In: Proc. of SODA 2002 (2002)

    Google Scholar 

  12. Kha, D.D., Yoshikawa, M., Uemura, S.: An XML indexing structure with relative region coordinate. In: Proc. of ICDE 2001 (2001)

    Google Scholar 

  13. Kimber, W.E.: HyTime and SGML: Understanding the HyTime HYQ query language 1.1. Technical report, IBM Corporation (1993)

    Google Scholar 

  14. Knuth, D.E.: The Stanford GraphBase: a platform for combinatorial computing. ACM Press, New York (1993)

    Google Scholar 

  15. Lee, Y.K., Yoo, S.J., Yoon, K.: Index structures for structured documents. In: Proc. Of ACM First International Conference on Digital Libraries (1996)

    Google Scholar 

  16. Lei, S., G.: A graph query language and its query processing. In: Proc. of ICDE 1999 (1999)

    Google Scholar 

  17. Li, Q., Moon, B.: Indexing and querying XML data for regular path expressions. In: Proc. of VLDB 2001 (2001)

    Google Scholar 

  18. Schenkel, R., Theobald, A., Weikum, G.: Hopi: An efficient connection index for complex xml document collections. In: Bertino, E., Christodoulakis, S., Plexousakis, D., Christophides, V., Koubarakis, M., Böhm, K., Ferrari, E. (eds.) EDBT 2004. LNCS, vol. 2992, pp. 237–255. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  19. Schenkel, R., Theobald, A., Weikum, G.: Efficient creation and incremental maintenance of the HOPI index for complex XML document collections. In: Proc. of ICDE 2005 (2005)

    Google Scholar 

  20. Schmidt, A., Waas, F., Kersten, M., Carey, M.J., Manolescu, I., Busse, R.: Xmark: A benchmark for xml data management. In: Proc. of VLDB 2002 (2002)

    Google Scholar 

  21. Tatarnov, I., Viglas, S.D., Beyer, K., Shanmugasundaram, J., Shekita, E., Zhang, C.: Storing and quering ordered XML using a relational database system. In: Proc. of SIGMOD 2002 (2002)

    Google Scholar 

  22. Wang, H., He, H., Yang, J., Yu, P.S., Yu, J.X.: Dual labeling: Answering graph reachabilityqueries in constant time. In: Proc. of ICDE 2006 (2006)

    Google Scholar 

  23. Wang, W., Jiang, H., Lu, H., Yu, J.: Pbitree coding and efficient processing of containment join. In: Proc. of ICDE 2003 (2003)

    Google Scholar 

  24. YoshiKawa, M., Amagasa, T.: XRel: A path-based approach to storage and retrieval of XML documents using relational databases. ACM Transactions on Internet Technology 1(1) (2001)

    Google Scholar 

  25. Zhang, C., Naughton, J.F., DeWitt, D.J., Luo, Q., Lohman, G.M.: On supporting containment queries in relational database management systems. In: Proc. of SIGMOD 2001 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cheng, J., Yu, J.X., Lin, X., Wang, H., Yu, P.S. (2006). Fast Computation of Reachability Labeling for Large Graphs. In: Ioannidis, Y., et al. Advances in Database Technology - EDBT 2006. EDBT 2006. Lecture Notes in Computer Science, vol 3896. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11687238_56

Download citation

  • DOI: https://doi.org/10.1007/11687238_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32960-2

  • Online ISBN: 978-3-540-32961-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics