On Trade-Offs in External-Memory Diameter-Approximation

  • Ulrich Meyer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)


Computing diameters of huge graphs is a key challenge in complex network analysis. However, since exact diameter computation is computationally too costly, one typically relies on approximations. In fact, already a single BFS run rooted at an arbitrary vertex yields a factor two approximation. Unfortunately, in external-memory, even a simple graph traversal like BFS may cause an unacceptable amount of I/O-operations. Therefore, we investigate alternative approaches with worst-case guarantees on both I/O-complexity and approximation factor.


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  1. 1.
    Abello, J., Buchsbaum, A., Westbrook, J.: A functional approach to external graph algorithms. Algorithmica 32(3), 437–458 (2002)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Communications of the ACM 31(9), 1116–1127 (1988)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Arge, L., Brodal, G., Toma, L.: On external-memory MST, SSSP and multi-way planar graph separation. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 433–447. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Arge, L., Meyer, U., Toma, L.: External memory algorithms for diameter and all-pairs shortest-paths on sparse graphs. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 146–157. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Atallah, M., Vishkin, U.: Finding Euler tours in parallel. Journal of Computer and System Sciences 29(30), 330–337 (1984)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Boitmanis, K., Freivalds, K., Ledins, P., Opmanis, R.: Fast and simple approximation of the diameter and radius of a graph. In: Àlvarez, C., Serna, M.J. (eds.) WEA 2006. LNCS, vol. 4007, pp. 98–108. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Buchsbaum, A., Goldwasser, M., Venkatasubramanian, S., Westbrook, J.: On external memory graph traversal. In: Proc. 11th Ann. Symposium on Discrete Algorithms (SODA), pp. 859–860. ACM-SIAM (2000)Google Scholar
  8. 8.
    Chiang, Y.J., Goodrich, M.T., Grove, E.F., Tamasia, R., Vengroff, D.E., Vitter, J.S.: External memory graph algorithms. In: Proc. 6th Ann.Symposium on Discrete Algorithms (SODA), pp. 139–149. ACM-SIAM (1995)Google Scholar
  9. 9.
    Chowdury, R., Ramachandran, V.: External-memory exact and approximate all-pairs shortest-paths in undirected graphs. In: Proc. 16th Ann. Symposium on Discrete Algorithms (SODA), pp. 735–744. ACM-SIAM (2005)Google Scholar
  10. 10.
    Cormen, T.H., Leiserson, C., Rivest, R.: Introduction to Algorithms. McGraw-Hill, New York (1990)Google Scholar
  11. 11.
    Magnien, C., Latapy, M., Habib, M.: Fast computation of empirically tight bounds for the diameter of massive graphs (2007), http://www-rp.lip6.fr/~latapy/Diameter/
  12. 12.
    Mehlhorn, K., Meyer, U.: External-memory breadth-first search with sublinear I/O. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 723–735. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Meyer, U., Sanders, P., Sibeyn, J. (eds.): Algorithms for Memory Hierarchies. LNCS, vol. 2625. Springer, Heidelberg (2003)MATHGoogle Scholar
  14. 14.
    Meyer, U., Zeh, N.: I/O-efficient undirected shortest paths. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 434–445. Springer, Heidelberg (2003)Google Scholar
  15. 15.
    Munagala, K., Ranade, A.: I/O-complexity of graph algorithms. In: Proc. 10th Ann. Symposium on Discrete Algorithms (SODA), pp. 687–694. ACM-SIAM (1999)Google Scholar
  16. 16.
    Vitter, J.S.: External memory algorithms and data structures: Dealing with massive data. ACM computing Surveys 33, 209–271 (2001), http://www.cs.purdue.edu/homes/~jsv/Papers/Vit.IO_survey.pdf CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ulrich Meyer
    • 1
  1. 1.Institute for Computer ScienceJ.W. Goethe UniversityFrankfurt/MainGermany

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